The integer n is equal to k^2 for some integer k. If n is divisible by 24 and by 10, what is the smallest possible positive value of n ?
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If n is a perfect square divisible by 24 and 10, then it needs to have all the prime factors of 24 and 10 in pairs. The prime factorization of 24 is and the prime factorization of 10 is .
Conveniently, the three 2s in 24 and the one 2 in 10 make two pairs of 2s, but in order to make a perfect square with all those factors, you’re going to need to add another 3 and another 5. So the smallest n could be, if it has to be a perfect square, is .
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