Prove that $l = k/\gcd(m,k)$.

Question

Suppose $ml = kt$ where $t$ is an integer and $m<k.$

$\implies k~|~ml$ $~~~~~$and $~~~~~$ $1 \leq \gcd(m,k) \leq m$

$\implies \dfrac{k}{\gcd(m,k)}~\Big|~\left(\dfrac{m}{\gcd(m,k)}\right)l$

What am I missing?