jmc

Since $12=2^2\cdot 3$ and $15=3\cdot 5$ are factors of $x$, $x$ must be divisible by the least common multiple of 12 and 15, which is $2^2\cdot 3\cdot 5$. Since $x$ has 12 factors and the LCM has $(2+1)(1+1)(1+1)=12$ factors, $x=2^2\cdot 3\cdot 5=\boxed{60}$.