Let $m,n \in \mathbb{N}$ with $m \ge 1$ and $n \ge 1$. Regard $\mathbb{Z}/m\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$ as additive groups. Then the direct product group $\mathbb{Z}/m\mathbb{Z} \times \mathbb{Z}/n\mathbb{Z}$ is cyclic if and only if $\gcd(m,n)=1$. If $\gcd(m,n)=1$, then