Answer is 161 but it doesn't make sense. 161 is not even a perfect square. Sorry for the scribbles.
#help (prime number, HCF and LCM question)
crude tendon
hushed juniperBOT
Answer is 161 but it doesn't make sense. 161 is not even a perfect square. Sorry...
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crude tendon
Would appreciate if anyone could explain how they arrived at the answer as I am totally clueless. The "correct" solution on the answer key is just 7 x 23 = 161.
crystal shell
Maybe they meant 161^2, rather?
crude tendon
nope it's just 161
so i think the answer key is wrong but i have no idea how to do this either
crystal shell
Well, note that the prime powers of gcd(x, y) are just minima of prime powers of x and y. Similar for lcm(x, y), but this time they are maxima.
So, both x and y have factors of 7 and 23 to the power of at least 1. So, their LCM must also contain them.
As they must be in k, that means k is divisible by 7 and 23. But since k is a square, it must be divisible by their squares.
So, the smallest value of k is 7^2*23^2 = 161^2.