Suppose that $a$ and $b$ are positive integers for which $a$ has $3$ factors and $b$ has $a$ factors. If $b$ is divisible by $a$, what is the least possible value of b?
If a has 3 factors, then a will be the square of a prime number (it's factors are 1, a prime number, and the square of the prime number). The smallest square of a prime number is 2^2 = 4. Therefore, if b is divisible by 4 and has 4 factors, than the least possible value of b is 8.