Wikipedia says:
More generally, a semidirect product of any two cyclic groups $C_m$ with generator $a$ and $C_n$ with generator $b$ is given by one extra relation, $aba^{−1} = b^k$, with $k$ and $n$ coprime; that is, the presentation:
$$\langle a, b| a^m = e, b^n = e, aba^{-1} = b^k\rangle$$
Why must $k$ and $n$ be co-prime in this context?