gmat prep

Mclaughlin wrote:If X is a positive integer, what is the Least common multiple of X, 6, 9

1. the least common mulitple of x and 6 is 30
2. the least common multiple of x and 9 is 45

the OA is D but i got it to be C because I thought X could be either 5 or 15.

someone help?

I actually got the same answer for the same reason. X could be either 5 or 15. Interesting!

X could be 5 or 15 but the LCM of X,6,9 doesn't change if X is 5,15 or even 45.

Hence IMO D.

Please correct me if I'm wrong.

I agree with D
Question is not about the value of x, it is about the LCM of three intergers

The key here is prime factorisation
rephrasing the main statement:
What is LCM of x, 2*3 (6=2*3), and 3^2 (9=3*3)

(1)
LCM of x and 2*3 is 30.
Factoring 30=2*3*5
this means that x has 5 as a factor. x can contain 2 and 3 but not necessary
answering the main question:
LCM of 2*3, 3^3 and x is 2*3^2*5=90
Let's check
x=5. LCM of 5, 6 and 9 is 90
x=10. LCM = 90
x=15. LCM = 90
SUFF

(2)
Using the same logic
LCM of x and 3^2 is 45
45 = 3^2*5
x has 5 as a factor
LCM of 5, 6 and 9 is 90
SUFF

Answer D

Remember,
that
LCM of 2 or more numbers is a product of all prime numbers, included into prime factorization at least one of these numbers, raised to the highest of two powers

GCD of 2 or more numbers is a product of prime numbers, included into prime factorization of all numbers, and raised to the smallest of two powers