what is the order of if and are disjoint cycles of length 4

what is the order of if and are disjoint cycles of length 4 and 6. respectively?(Explain why,use the fact that disjoint cycles commute)

Solution

The order of a permutation of a finite set written in disjoint cycle form is the least common multiple of the lengths of the cycles. The least common multiple of 4 and 6 being 12, the order of is 12.