Problem Solving

realanoop wrote:k is a positive integer and 225 and 216 are both divisors of k. If k=2^a*3^b*5^c, where a, b and care positive integers, what is the least possible value of a+ b+ c?
(A) 4(B) 5(C) 6(D) 7(E) 8

ans is 6 or 8?

In a question that mentions divisors, you'll almost always want to prime factorize:

225 = 15^2 = 3^2 * 5^2
216 = 6^3 = 2^3 * 3^3

So we know k is divisible by 2^3 * 3^3 * 5^2. The answer is thus 8. Note that this question is really just asking about the Least Common Multiple of 225 and 216, which is what we found.