Answer
Let $a$, $b$, and $c$ be integers such that $a|b$. Then by the definition of divisibility, $b=ka$ for some integer $k$. Multiplying both sides of the equation by $c$, we get that $bc=(ka)c=(kc)a$, where $kc$ is an integer because $k$ and $c$ are both integers. Therefore, by the definition of divisibility, $a|bc$.
Work Step by Step
We know that $(ka)c=(kc)a$ by the associative and commutative properties of multiplication, and that $kc$ is an integer by the closure of the integers under multiplication.