If the LCM of a & 12 is 36 what could be the possible values of a?

The LCM of 12 and a contains two 2's. Since the LCM contains each prime factor to the power it appears the MOST, we know that a cannot contain more than two 2's.

LCM of 12 and a contain two 3's. But 12 only contains one 3. The 3^2 factor in the LCM must have come from prime factorization of a. Thus we know that a contains exactly two 3's.

Since a must contain exactly two 3's nd can contain no 2's, one 2 or two 2's a could be

3*3=9

3*3*2=18

3*3*2**2=36.

Thus 9,18 and 36 are three values.

I am struggling to understand the concept.

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Best Regards,

E.

MGMAT 1 --> 530

MGMAT 2--> 640

MGMAT 3 ---> 610

GMAT ==> 730