# Commutative Algebra/The lattice of submodules, Noether isomorphism theorems

• Let ${\displaystyle m,n\in \mathbb {N} }$. Prove that ${\displaystyle (m\mathbb {Z} )/(n\mathbb {Z} )\cong \mathbb {Z} {\big /}{\frac {n}{\gcd(m,n)}}\mathbb {Z} }$.