Suppose $a$ and $b$ are positive integers such that the units digit of $a$ is $2$, the units digit of $b$ is $4$, and the greatest common divisor of $a$ and $b$ is $6$. What is the smallest possible value of the least common multiple of $a$ and $b$?
Here are a couple of candidates:
a =12 and b=54
GCD[12, 54] =6
LCM[12, 54] =108
Also a =42 and b= 24 will give the same GCD of 6, but the LCM[42, 24] =168 which is > than the first one.
