Is it true or false?
If $a$ is a permutation that is an $m$-cycle and $b$ is the permutation that is $n$-cylce then order of $ab = \operatorname{lcm}(m,n)$.
2026-04-03 14:26:06.1775226366
Order of a product of two cycles
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If the cycles are disjoint, your statement is true.
For non-disjoint cycles, a counterexample is given by $$ \operatorname{ord}((12)(23)) = \operatorname{ord}((123)) = 3. $$