The order of a permutation is the lcm of its disjoint cycle lengths

Let $\sigma$ be a permutation in $S_n$. Let $\sigma=\sigma_1\sigma_2\cdots\sigma_k$, where $\sigma_1,\dots, \sigma_k$ are disjoint cycles of lengths $l_1,\dots,l_k$ respectively. Then the order of $\sigma$ is equal to: