AMC 8 2016 Problem 20

The least common multiple of $a$ and $b$ is $12$, and the least common multiple of $b$ and $c$ is $15$. What is the least possible value of the least common multiple of $a$ and $c$? $\textbf{(A) }20 \textbf{(B) }30 \textbf{(C) }60 \textbf{(D) }120 \textbf{(E) }180$