Prove that if $3\mid n$ ($n$ is a multiple of $3$) and $5\mid n$, then $15\mid n$.
So far I have the following incomplete proof:
Suppose that $3\mid n$ and $5\mid n$, then $∃k,l∈ℤ$ such that $n=3k$ and $n=5l$.
Now, $3k=5l$ $...?$
From here, I struggle to deduce further to show that the conclusion is true. I know that I should show that $n$ is a multiple of $15$ in some way.