Show $\operatorname{Hom}_{\mathbb{Z}}\left ( \mathbb{Z}/n\mathbb{Z},\mathbb{Z}/m\mathbb{Z} \right )\cong \mathbb{Z}/\left ( n,m \right )\mathbb{Z}$
Describe explicitly $\operatorname{Hom}_{\mathbb{Z}}(\mathbb{Z}_n, \mathbb{Z}_m)$.