HI

Let $\zeta_m$ be a primitive $m^\text{th}$ root of unity, and let $\zeta_n$ be a primitive $n^\text{th}$ root of unity. Then $\zeta_m\zeta_n$ is a primitive $\ell^\text{th}$ root of unity for some positive integer $\ell.$

What can we say about $\ell$ in general?

Clarification: In the answer choices, $\gcd(\cdot)$ and $\text{lcm}(\cdot)$ denotes the greatest common divisor function and the lowest common multiple function.\