Count of Distinct Homomorphisms between Additive Groups of Integers Modulo m

Theorem
Let $m, n \in \Z_{>0}$ be (strictly) positive integers.

Let $\struct {\Z_m, +}$ denote the additive group of integers modulo $m$.

The number of distinct homomorphisms $\phi: \struct {\Z_m, +} \to \struct {\Z_n, +}$ is $\gcd \set {m, n}$.