LCM and HCF | Mathematics | Page 1

silent oasis Jan 28, 2026, 1:35 PM

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i need a refresh on this beacause its hard to find the lcm on big numbers

fluid groveBOT Jan 28, 2026, 1:35 PM

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brazen gull Jan 28, 2026, 1:37 PM

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what is your current method of finding LCMs?

silent oasis Jan 28, 2026, 1:38 PM

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let me show u

brazen gull Jan 28, 2026, 1:38 PM

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do note that no matter what your method of finding LCMs are, large numbers are computationally expensive to compute the LCMs of.

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because, well... they are large.

silent oasis Jan 28, 2026, 1:39 PM

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this

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is there a trick to find it easily?

brazen gull Jan 28, 2026, 1:39 PM

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the general trick is to use prime factorizations.

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but there is one shortcut you can make under one specific circumstance.

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if all of your numbers do not share any common factors (other than 1 of course), the LCM of that set of numbers can be found by multiplying them together.

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but otherwise, prime factorization is your best bet.

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and as a bonus, the prime factorization method works to find the HCF as well, with a minor tweak.

silent oasis Jan 28, 2026, 1:41 PM

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what is prime fcatorizations? sorry im dumb im trying to be good in maths but i cant understand it much

brazen gull Jan 28, 2026, 1:41 PM

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no worries! we'll take it slowly.

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first, do you know what prime numbers are?

silent oasis Jan 28, 2026, 1:42 PM

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uh

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2,3,5,7,9,11

brazen gull Jan 28, 2026, 1:43 PM

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9 is not prime.

silent oasis Jan 28, 2026, 1:43 PM

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oh

brazen gull Jan 28, 2026, 1:43 PM

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but more importantly, do you know the definition of a prime number?

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in other words, do you know what makes a number prime?

silent oasis Jan 28, 2026, 1:43 PM

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no..

brazen gull Jan 28, 2026, 1:43 PM

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alright.

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prime numbers are numbers that can only be divided by 1 and itself.

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this is why 9 is not a prime - it can be divided by 3.

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the rest of the numbers on your list are indeed prime, though.

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now, separately, do you know what the factorization of a number is?

silent oasis Jan 28, 2026, 1:45 PM

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nope

brazen gull Jan 28, 2026, 1:45 PM

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alright.

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do you agree with me if I say that, for example, 18 = 9 x 2?

silent oasis Jan 28, 2026, 1:46 PM

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yes

brazen gull Jan 28, 2026, 1:46 PM

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good! this is an example of a factorization for a number - breaking a number down into two (or more) numbers multiplied together.

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3 x 6 is also a possible factorization for 18, so you might wonder, how do we know which factorization to use for the LCM?

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the answer is, we don't need to rely on this. that's where prime factorization comes into play.

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now, let's take 9 x 2 as an example.

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we know this gives us 18. but can either 9 or 2 be broken down further?

silent oasis Jan 28, 2026, 1:47 PM

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nope

brazen gull Jan 28, 2026, 1:48 PM

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are you sure?

silent oasis Jan 28, 2026, 1:48 PM

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9 can actaully but not 2

brazen gull Jan 28, 2026, 1:48 PM

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brazen gull this is why 9 is not a prime - it can be divided by 3.

^^^

silent oasis Jan 28, 2026, 1:48 PM

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hmm

brazen gull Jan 28, 2026, 1:48 PM

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silent oasis 9 can actaully but not 2

alright, good! remember that I asked if either 9 or 2 can be broken down further.

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I never specified that both of them have to be.

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so 9 can be broken down further, and I trust you agree with me that it would be 3 x 3.

silent oasis Jan 28, 2026, 1:48 PM

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yes

brazen gull Jan 28, 2026, 1:49 PM

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so, we went from 18 = 9 x 2 = 3 x 3 x 2.

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now in that last set of numbers, can any of them be broken down further?

silent oasis Jan 28, 2026, 1:49 PM

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silent oasis Jan 28, 2026, 1:50 PM

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brazen gull now in that last set of numbers, can any of them be broken down further?

9?..

brazen gull Jan 28, 2026, 1:50 PM

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no, we have 3 x 3 x 2.

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can any of these numbers be broken down further?

silent oasis Jan 28, 2026, 1:50 PM

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nope

brazen gull Jan 28, 2026, 1:51 PM

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bingo! these three numbers are all prime, and therefore cannot be broken down any further.

silent oasis Jan 28, 2026, 1:51 PM

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okay

brazen gull Jan 28, 2026, 1:51 PM

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but wait, you might ask! what about 3 x 6, right?

silent oasis Jan 28, 2026, 1:51 PM

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yes

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how did u get it?

brazen gull Jan 28, 2026, 1:51 PM

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silent oasis how did u get it?

multiplication tables.

silent oasis Jan 28, 2026, 1:52 PM

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oh yeah 3 x 6 is 18

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sorry

brazen gull Jan 28, 2026, 1:52 PM

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right.

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so, if we took 3 x 6 earlier, we can break down 6 into 3 x 2, and that still gives us 3 x 3 x 2.

silent oasis Jan 28, 2026, 1:52 PM

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how do u get it 2?

brazen gull Jan 28, 2026, 1:52 PM

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I'm sorry?

silent oasis Jan 28, 2026, 1:52 PM

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how did u get the 2?

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which made 3x2

brazen gull Jan 28, 2026, 1:53 PM

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the 6.

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please tell me you agree with me that 6 = 3 x 2?

silent oasis Jan 28, 2026, 1:53 PM

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yes i agree

brazen gull Jan 28, 2026, 1:53 PM

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then we have 3 x 6 = 3 x (3 x 2), and that's it.

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you may be smelling a rat right about now. we got the same sequence of numbers - 3 x 3 x 2 - no matter how we break down 18 initially.
this is why we work with prime factorizations - every number has a unique prime factorization.

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there is a proof for this but it's too early to show it right now.

fervent portal Jan 28, 2026, 1:54 PM

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brazen gull there is a proof for this but it's too early to show it right now.

can i see it please??

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not right now if it’s inconvenient

brazen gull Jan 28, 2026, 1:55 PM

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fervent portal can i see it please??

you can open your own thread and ask about it if you wish to. I am not about to mess up the OP with a wall of text.

fervent portal Jan 28, 2026, 1:55 PM

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got it thanks

brazen gull Jan 28, 2026, 1:55 PM

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anyway, since every number has a unique way of breaking it down into primes, we can skip worrying about "but what if we broke down the number this way?".

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so, let's get back to LCM.

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suppose I asked you to find the LCM of, say 12 and 18.

silent oasis Jan 28, 2026, 1:56 PM

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yeah

brazen gull Jan 28, 2026, 1:56 PM

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before even thinking about finding the LCM of these two numbers, let's break them down into primes first.

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you know that 18 = 3 x 3 x 2.
now, do the same for 12.

silent oasis Jan 28, 2026, 1:56 PM

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may i do it first?

brazen gull Jan 28, 2026, 1:57 PM

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sure!

silent oasis Jan 28, 2026, 1:57 PM

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on paint

brazen gull Jan 28, 2026, 1:57 PM

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but don't try to find the LCM yet. just break 12 down into primes.

silent oasis Jan 28, 2026, 1:57 PM

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so like u did for 18?

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ok nvm i dont get it

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how do u get the prime

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beacuse 6x2 is 12

brazen gull Jan 28, 2026, 1:59 PM

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silent oasis beacuse 6x2 is 12

that is correct.

silent oasis Jan 28, 2026, 1:59 PM

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so if i brake it down 2 x 3 is 6

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breake*

brazen gull Jan 28, 2026, 1:59 PM

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yes.

silent oasis Jan 28, 2026, 1:59 PM

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holy spelling

brazen gull Jan 28, 2026, 1:59 PM

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so you have 6x2, and you know 6 = 2x3. what would you get after?

silent oasis Jan 28, 2026, 1:59 PM

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12 = 2x3x6?..

brazen gull Jan 28, 2026, 2:00 PM

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you already broke down the 6. it should not be there any more.

silent oasis Jan 28, 2026, 2:00 PM

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oh

brazen gull Jan 28, 2026, 2:00 PM

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I'll show you a way to keep track of your prime factorization.

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you can use the same method to help keep track of your prime factorization for 12.

silent oasis Jan 28, 2026, 2:01 PM

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ohh

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can u give me another number?

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ill try it on my own

brazen gull Jan 28, 2026, 2:02 PM

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sure. try prime factorizing 24.

silent oasis Jan 28, 2026, 2:02 PM

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okay

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i might be wrong

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wait i forgot to bring down the 2

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no

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nvm

brazen gull Jan 28, 2026, 2:05 PM

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can you write out your final prime factorization?

silent oasis Jan 28, 2026, 2:05 PM

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isnt that final?

brazen gull Jan 28, 2026, 2:05 PM

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write it in one line.

brazen gull Jan 28, 2026, 2:06 PM

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brazen gull no, we have 3 x 3 x 2.

like so.

silent oasis Jan 28, 2026, 2:06 PM

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brazen gull Jan 28, 2026, 2:06 PM

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just 3 x 2?

silent oasis Jan 28, 2026, 2:06 PM

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oh wait

brazen gull Jan 28, 2026, 2:07 PM

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don't forget the other terms you didn't break down!

silent oasis Jan 28, 2026, 2:07 PM

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im wrong.?

brazen gull Jan 28, 2026, 2:08 PM

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silent oasis Jan 28, 2026, 2:08 PM

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i bring that 2 down aswell?

brazen gull Jan 28, 2026, 2:08 PM

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yes, of course. bring down anything that has been fully broken down!

silent oasis Jan 28, 2026, 2:09 PM

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okay im fixing the question

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brazen gull Jan 28, 2026, 2:10 PM

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why is the 2 after the 6 sharing the same 2 as the 2 you got from breaking down the 6?

silent oasis Jan 28, 2026, 2:11 PM

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sorry

brazen gull Jan 28, 2026, 2:11 PM

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no worries, just questions to guide you onto the right step.

silent oasis Jan 28, 2026, 2:11 PM

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its wrong right?

brazen gull Jan 28, 2026, 2:11 PM

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yes, it's incorrect.

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if this method is still confusing, you can try this alternative method of notation.

silent oasis Jan 28, 2026, 2:12 PM

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i was taught this method so i can understand this easier

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but

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how did u get two 3?

brazen gull Jan 28, 2026, 2:12 PM

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from 24 or 18?

silent oasis Jan 28, 2026, 2:12 PM

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for the 24

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oh u did 18

brazen gull Jan 28, 2026, 2:13 PM

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the 24 will not have two 3s.

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look at my starting number.

silent oasis Jan 28, 2026, 2:13 PM

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but how is 3 x 2 wrong?

brazen gull Jan 28, 2026, 2:13 PM

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silent oasis but how is 3 x 2 wrong?

what's 3 x 2?

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is it 24?

silent oasis Jan 28, 2026, 2:13 PM

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no

brazen gull Jan 28, 2026, 2:13 PM

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there's the problem.

silent oasis Jan 28, 2026, 2:13 PM

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how do i fix it?

brazen gull Jan 28, 2026, 2:14 PM

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look at how I keep track of the 2s that were already broken down.
I made sure to carry all 2s from the previous step into the next.

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using the alternative method gives the same thing. maybe it's cleaner to look at.

silent oasis Jan 28, 2026, 2:15 PM

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oh

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can u give another number if possible? that i can try on my own

brazen gull Jan 28, 2026, 2:17 PM

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silent oasis Jan 28, 2026, 2:19 PM

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brazen gull Jan 28, 2026, 2:19 PM

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1 is not a prime!

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but otherwise yes, the prime factorization is correct!

silent oasis Jan 28, 2026, 2:20 PM

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what do i put after removing the 1?

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just 3?

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5x3x2?

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oh WAIT

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its correct both ways

brazen gull Jan 28, 2026, 2:20 PM

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you should have stopped here.

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5 is prime. it can't be broken down.

silent oasis Jan 28, 2026, 2:20 PM

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ok but i have a big problem for you

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my teacher gives me 3 dijit lcm

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how do i slove it easily

brazen gull Jan 28, 2026, 2:21 PM

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you mean digit*?

silent oasis Jan 28, 2026, 2:21 PM

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yes sorry

brazen gull Jan 28, 2026, 2:21 PM

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well, unfortunately, large LCMs are not feasible to solve by hand. you can still use this method, and then how fast it is depends on how fast you can break down the numbers.

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it remains the easiest method I know of to find LCMs generally.

silent oasis Jan 28, 2026, 2:21 PM

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for example

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teacher gave me the question to find the LCM of 725

brazen gull Jan 28, 2026, 2:22 PM

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725 and what?

silent oasis Jan 28, 2026, 2:22 PM

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pretty sure 77

brazen gull Jan 28, 2026, 2:22 PM

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you can't find the LCM of a single number!

silent oasis Jan 28, 2026, 2:22 PM

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i was in class thinking for a long time what is half of 725

brazen gull Jan 28, 2026, 2:22 PM

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okay, so 77 and 725.

brazen gull Jan 28, 2026, 2:23 PM

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silent oasis i was in class thinking for a long time what is half of 725

if you think you can halve 725, please don't.

silent oasis Jan 28, 2026, 2:23 PM

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halve meaning?

brazen gull Jan 28, 2026, 2:23 PM

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725 ends in a 5, which is odd. you shouldn't expect a whole number if you divide an odd number by 2.

brazen gull Jan 28, 2026, 2:23 PM

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silent oasis halve meaning?

halve = divide by 2.

silent oasis Jan 28, 2026, 2:23 PM

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oh

brazen gull Jan 28, 2026, 2:23 PM

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anyway, in this case...

silent oasis Jan 28, 2026, 2:24 PM

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i was thinking for a long time in class what times what is 725.

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is there an trick?

brazen gull Jan 28, 2026, 2:25 PM

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77 = 7 x 11, and there's no further breaking down for this,
now, 725 ends in a 5. numbers that end in a 5 are guaranteed to be divisible by 5, so try that first.
I get 725 = 145 x 5, and- hey, another number ending in 5! let's do that again!
that gives us 39 x 5 x 5.

note that the digits of 39 sum up to 12, which means it's divisible by 3. so break it down using 3 and we'll get 13 x 3 x 5 x 5, and we're done.

silent oasis Jan 28, 2026, 2:26 PM

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how did u 145 so fast

brazen gull Jan 28, 2026, 2:26 PM

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practice, unfortunately.

silent oasis Jan 28, 2026, 2:26 PM

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of division?

brazen gull Jan 28, 2026, 2:26 PM

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and a little pattern recognition.

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of both division and multiplication.

silent oasis Jan 28, 2026, 2:26 PM

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can u teach me division for numbers like these?

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so i can find it out easily

brazen gull Jan 28, 2026, 2:27 PM

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it's really just doing exercises and figuring out patterns.

silent oasis Jan 28, 2026, 2:27 PM

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oh

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is there a way u could teach me long division for this?

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its gonna make my life way easier

brazen gull Jan 28, 2026, 2:27 PM

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huh? didn't the other guy do so already?

silent oasis Jan 28, 2026, 2:28 PM

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his method confused me alot

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i was taught the long division method and he was taught an different

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so it was hard for us both to communicate

brazen gull Jan 28, 2026, 2:28 PM

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his method is the same as yours, actually.

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it's just that he writes it differently.

silent oasis Jan 28, 2026, 2:28 PM

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oh

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give me a 3 digit number

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foor LCM

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for*

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ill try to slove it

brazen gull Jan 28, 2026, 2:29 PM

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I don't think you should start practicing with that large of numbers yet...

silent oasis Jan 28, 2026, 2:29 PM

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but my teachers gives me large numbers

brazen gull Jan 28, 2026, 2:29 PM

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ever heard of "dream big, start small"?

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but if you insist, find the LCM of 110 and 25.

silent oasis Jan 28, 2026, 2:33 PM

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is this correct?

brazen gull Jan 28, 2026, 2:33 PM

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for 25, you could have stopped after breaking it down once.

silent oasis Jan 28, 2026, 2:34 PM

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so im wrong?

brazen gull Jan 28, 2026, 2:34 PM

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same for 110 - the last line is unnecessary (you can see that it's the same as the line above it).

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neither of them are wrong.

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both of them are correct, actually!

silent oasis Jan 28, 2026, 2:34 PM

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problem is

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when the teascher gives me odd numbers

brazen gull Jan 28, 2026, 2:34 PM

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but why these lines?

silent oasis Jan 28, 2026, 2:34 PM

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i didnt realize that before u told me

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anyways the teacher gives me 3 digit odd numbers

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how do i know what to multiply it so it equals that

brazen gull Jan 28, 2026, 2:35 PM

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check for divisibility by small odd numbers first.

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then work your way up.

silent oasis Jan 28, 2026, 2:36 PM

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meaning of divisibility?

brazen gull Jan 28, 2026, 2:37 PM

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if you can take a number, say A, and divide it by another number, say B, and the answer is a whole number, we say A is divisible by B.

silent oasis Jan 28, 2026, 2:38 PM

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oh

brazen gull Jan 28, 2026, 2:38 PM

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by the way, a personal comment - considering how much tutoring you need, I highly recommend finding a tutor or getting in touch more with your teacher.

silent oasis Jan 28, 2026, 2:38 PM

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problem is

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i already have an tutor

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but i get very shy asking her to explain it

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i barely talk to my other family members (expect mom dad)

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i just get shy idk why

brazen gull Jan 28, 2026, 2:39 PM

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mm, understandable, but personal tutors would be able to help you much more and much faster than most any helper can here.

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because they can diagnose issues on the spot.

silent oasis Jan 28, 2026, 2:40 PM

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i wanna tell u something..

brazen gull Jan 28, 2026, 2:40 PM

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maybe try to communicate with your tutor via writing?

silent oasis Jan 28, 2026, 2:40 PM

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when i get something wrong in math like 3 times my math tutor laughs or smiles

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so thats why i dont ask her to explain it

brazen gull Jan 28, 2026, 2:41 PM

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what would be wrong with smiling? are they condescending? do they explain to you after the fact?

silent oasis Jan 28, 2026, 2:42 PM

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no they dont explain only some times

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but forget that

silent oasis Jan 28, 2026, 2:42 PM

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brazen gull if you can take a number, say A, and divide it by another number, say B, and the...

can u give an explain if possible?

brazen gull Jan 28, 2026, 2:42 PM

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I'm mentioning this because there is no way I can teach you all of arithmetic. I'm a helper, not a tutor.

brazen gull Jan 28, 2026, 2:43 PM

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silent oasis can u give an explain if possible?

6 divided by 3 = 2. since 2 is a whole number, we say that 6 is divisible by 3.

silent oasis Jan 28, 2026, 2:44 PM

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possible explain with 3 digit numbers?

loud dawn Jan 28, 2026, 2:45 PM

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yeah smth like 525

brazen gull Jan 28, 2026, 2:45 PM

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125 / 5 = 25. therefore, 125 is divisible by 5.

silent oasis Jan 28, 2026, 2:45 PM

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okay ty

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can you give an question that i could try on my own?

brazen gull Jan 28, 2026, 2:46 PM

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of LCM? or prime factorization?

silent oasis Jan 28, 2026, 2:46 PM

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LCM

brazen gull Jan 28, 2026, 2:46 PM

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brazen gull but if you insist, find the LCM of 110 and 25.

well you haven't given me the answer to this, so this can be the example question.

silent oasis Jan 28, 2026, 2:47 PM

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okay

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i have to go eat dinner.

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thanks for explaning to me

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ill look forward to this tomorrow

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to revise it

brazen gull Jan 28, 2026, 2:56 PM

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sure. have a nice meal!

rose sequoia Jan 29, 2026, 6:08 AM

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I’m gonna assume the problem’s sorted

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But yeah, prime factorisation

#LCM and HCF