Hi VJesus12,

We're told that the least common multiple of positive integers M and N is 120 and M:N=3:4. We're asked for the greatest common factor of M and N. If you don't immediately see how to best approach a question, then you should consider 'brute force' - so you can then define what patterns are involved and get to the correct answer without spending too much time 'staring' at it.

Since M and N are in the ratio of 3 to 4, the two values could be....
M=3 and N=4. In this situation, the least common multiple would be 12 (re: 3x4 and 4x3)
M=6 and N=8. In this situation, the least common multiple would be 24 (re: 6x4 and 8x3)
M=9 and N=12. In this situation, the least common multiple would be 36 (re: 9x4 and 12x3)

At this point, you should recognize that the multiples follow a pattern: You'll need to multiply M by 4 and N by 3 to get the least common multiple. The prompt tells us that the LCM is supposed to be 120, so M and N must be....
M=30 and N=40

From here, you can find the Greatest Common Factor:
Factors of 30: 1&30, 2&15, 3&10, 5&6
Factors of 40: 1&40, 2&20, 4&10, 5&8
The GCF is 10

Final Answer: D

GMAT assassins aren't born, they're made,
Rich