If X is a positive integer...

[I_need_a_700plus]

Can someone explain the following data sufficiency problem from GMAT Prep Practice exam?

If x is a positive integer, what is the least common multiple of x, 6, and 9?

1) The least common multiple of x and 6 is 30.
2) The least common multiple of x and 9 is 45.

Answer: D

[RonPurewal]

First, tell us what you did and didn't understand, and what you tried. (If you just post a problem with no commentary, then the best answer is "Check out the answer key.")

[I_need_a_700plus]

Hi Ron,

In regards to statement 1, does this mean x = 5? If so, the LCM of x, 6, 9 = 270?

And as for statement 2, x = 5?, then the LCM of x, 6, 9 = 270 (again)?

[RonPurewal]

Statement 1 means that, of all the numbers that x and 6 go into, the smallest is 30.
This could mean that x = 5, but it could also mean that x = 10, 15, or 30.

Statement 1 means that, of all the numbers that x and 9 go into, the smallest is 45.
This could mean that x = 5, but it could also mean that x = 15 or 45.

Notice, though -- If you realize that LCM just means "biggest number that everyone goes into", then you don't have to think about individual values of x.
Once you have statement 1, you know that x and 6 both go into 30, and not into any smaller number. So, instead of thinking about the LCM of x, 6, and 9 individually, you can just think about the LCM of 30 and 9.
Analogously for statement 2.