If $(m, n) = 1$, then $\dfrac{\mathbb Z \times \mathbb Z}{\langle (m,n)\rangle}\cong\mathbb Z$

Question

How to show that

If $(m, n) = 1$, then $\dfrac{\mathbb Z \times \mathbb Z}{\langle (m,n)\rangle}\cong\mathbb Z$.

(Note: We consider this in group theory.)

I know that $(m, n) = 1$ means that $\exists x,y \in \mathbb{Z}: mx + ny = 1$.

How to find a group homomorphism $f: \mathbb Z \times \mathbb Z \to \mathbb{Z}$ whose kernel is ${\langle (m,n)\rangle}$?