Maximal period of a permutation

Question

To calculate the maximal order of an element of the symmetric group $S_5$, I reasoned this way: if $\pi = \sigma_1 \cdots\sigma_t$ is a product of disjoint cycles (with orders $k_1,\dots, k_t$) then the order of $\pi$ is the least common multiple of $k_1,\dots, k_t$. By case-checking and symbol pushing, I was able to find that the maximal order of an element of $S_5$ is 6 (I noticed that $\pi$ can be written as (a b) or (a b c) or (a b c d) or (a b c d e) or (a b) (c d) or (a b)(c d e)). Is there way to calculate this number in general?