Order_of_Product_of_Disjoint_Permutations_v2

Let $S_n$ denote the symmetric group on $n$ letters. Let $\pi$ be a product of disjoint permutations of orders $k_1, k_2, \ldots, k_r$. Then $\order \pi = \lcm \set {k_1, k_2, \ldots, k_r}$ where $\order \pi$ denotes the order of $\pi$ in $S_n$ $\lcm$ denotes lowest common multiple.