jmc

Since $a$ has three factors, it is the square of a prime. The smallest such square is $a=2^2=4,$ so we look to find the smallest positive integer $b$ with $4$ factors. The smallest positive integers with four factors are 6 and 8, of which $\boxed{8}$ is divisible by 4. It is easy to check that no smaller value of $b$ would work for a different choice of $a$, because the next smallest square is 9, which is greater than 8.