Data Sufficiency

What is LCM of X, 6, and 9

1. LCM of X and 6 is 30
2. LCM of X and 9 is 45


Answer is D. any help here appreciated.

IMO D
1) X can be 5,15 or 30
in all cases LCM of x,6,and 9 is 90

2)X can be 5,15,45
in all cases LCM is 90

1.) LCM of X,6 = 30 => x has to be 5 => so can find LCM of x,6,9 --> Suff

2.) Same logic, x = 5, hence can find the LCM of x,6,9--> Suff

Ans: D

Is the easiest way to do this problem create prime boxes for each? The MGMAT strategy guide uses a really complex system to figure out the possible overlap (a chart listing the prime factors and taking the highest power of each.)

If you use prime boxes, do you assume that the LCM holds ALL shared prime factors? Thus, any leftover (in this case, 5) are automatically attributed to X?