Showing that if $d=\gcd(n,m)$ then the integers $\frac{n}{d}$ and $\frac{m}{d}$ are coprime

Question

I'm having trouble understanding the indicated line from the solutions

Do a proof by contradiction by assuming there exists an $a > 1$ such that $a \mid \frac{n}{d}$ and $a \mid \frac{m}{d}$.

This implies (I don't understan why!) $ad\mid n$ and $ad\mid m$,

but $ad>d = \gcd(m,n)$, a contradiction.