What does "the LCM of two distinct positive integers is divisible by the highest single digit power of 3 , while their HCF is 12. " mean?

Question

The LCM of two distinct positive integers is divisible by the highest single digit power of 3 , while their HCF is 12. Which of the following could be the smaller of the two?

I think this means the LCM is divisible by $3^9$ but their HCF is 12.

So, one is $3 \cdot 2^2$, another is $3^{8+x} \cdot 2^2$ where $x \geq 0$?

A. 6

B. 24

C. 36

D. 300

E. 360

I heard B, and D are both correct but I don't see why.