linguistic:paraphrasing
Order of a permutation

The order of a permutation σ {\displaystyle \sigma } is the smallest positive integer m so that σ m = i d {\displaystyle \sigma ^{m}=\mathrm {id} }. It is the least common multiple of the lengths of its cycles. For example, the order of σ = (152) (34) {\displaystyle \sigma =(152)(34)} is lcm (3, 2) = 6 {\displaystyle {\text{lcm}}(3,2)=6}.