The greatest common divisor of AB is 12, the least common multiple is 72, a = 36, B =?

The greatest common divisor of AB is 12, the least common multiple is 72, a = 36, B =?

B=24
If the least common multiple is 72, then 72 must be a multiple of a and B,
The greatest common divisor is 12. We should also ensure that 12 is the common divisor of a and B
So B can only be 72, 36, 24, 12,
If B = 72, the least common multiple is 72 and the greatest common divisor is 36
If B = 36, the least common multiple is 36 and the greatest common divisor is 36
If B = 24, the least common multiple is 72 and the greatest common divisor is 12
If B = 12, the least common multiple is 36 and the greatest common divisor is 12