Show that if $(a,b)=1$, $a\mid c$ and $b\mid c$, then $a\cdot b\mid c$ 
Show that if $(a,b)=1$, $a\mid c$ and $b\mid c$, then $a\cdot b\mid c$.

Tried
$c=a\cdot k$ and $c=b\cdot j$ with $k,j\in\mathbb{N}$ then $a\cdot b\mid c^2=c\cdot c$.

$c=a.k=b.j$ 
But $(a,b)=1$, and $a$ divides $b.j$, so $a$ divides $j$. Hence $a.b$ divides $c$.
