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6 or 8?

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by realanoop » Tue Dec 30, 2008 11:57 am
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?
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Re: 6 or 8?

by Ian Stewart » Tue Dec 30, 2008 12:03 pm
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.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by rajataga » Tue Dec 30, 2008 12:52 pm
I found the LCM 5400, and then broke it up into

2^3
3^3
5^2

However, Ian's solution is quicker.
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by vittalgmat » Wed Dec 31, 2008 4:48 am
thanks Ian for the explanation.
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