vinviper1 wrote:Is the integer x divisible by 36?
1 x is divisible by 12
2 x is divisible by 9
I got this sort of the long way. How does the prime factorization process work on this one? I am trying to perfect this process. Thanks.
There are quite a few questions like this in older GMAT practice materials, so it's worth knowing how to approach it. I hope it's clear that neither statement is enough on its own (e.g. from Statement (1), x might be ...-12, 0, 12, 24, 36, etc, so might be divisible by 36, and might not).
If you look at both together, you know that x is divisible by 12
and by 9. What does this mean? It means exactly that x is divisible by the Least Common Multiple of 9 and 12. The LCM of 9 and 12 is 36; the two statements tell you exactly that x is divisible by 36, and are sufficient together: C is the answer.
You might need to use prime factorizations in a question like this to find the LCM, but with numbers as small as 9 and 12, you should probably be able to find the LCM without factoring. Still:
9 = 3^2
12 = 2^2 * 3
LCM = product of these primes to their highest powers = 2^2 * 3^2 = 36. If you need a review of how to find LCMs from prime factorizations, please do look this up in any decent book- there are several different ways to think about the process, and it's worth seeing them all to find the one that is most intuitive for you.
