 Order of a permutation

The order of a permutation $\pi$ is the least positive integer $m$ for which ${\pi }^m$ is the identity permutation. If its disjoint permutation cycles have lengths ${\ell }_1,\dots ,{\ell }_r$, thenIndeed a point in an $\ell$-cycle returns exactly after a multiple of $\ell$ steps, so all points return exactly at common multiples. The permutation $(123)(45)$ has order six, while its five moved labels do not by themselves determine its order. The identity permutation has order one.