$\pi$ permutation decomposed in $k$ disjoint cycles of length $n-1, \dots, n_k$. Find the order of $\pi$

Question

I'm currently working in the following excercise:

Suppose $\pi$ is the permutation that can be decomposed in $k$ disjoint cycles of length $n_1, \dots, n_k$. Find the order of $\pi$.

I know how to calculate a permutation order but I'm not sure about the calculation of a permutation of disjoint cycles of length $n_1, \dots, n_k$ order.

Thanks in advance for any hint or help.

Answer 1

Since the order of a $k$-cycle is $k$, you need $\operatorname {lcm}(n_1,\dots,n_k)$.

This is pretty much immediate, since disjoint cycles commute.