Intersection of Congruence Classes

Theorem
Let $$\mathcal{R}_m$$ denote congruence modulo $m$ on the set of integers $$\Z$$.

Then $$\mathcal{R}_m \cap \mathcal{R}_n$$ denotes congruence modulo $\mathrm{lcm} \left\{{m, n}\right\}$, where $$\mathrm{lcm} \left\{{m, n}\right\}$$ is the lowest common multiple of $$m$$ and $$n$$.