Products Of Primitive Roots Of Unity

Let ζm \zeta_m be a primitive mthm^\text{th} root of unity, and
let ζn \zeta_n be a primitive nth n^\text{th} root of unity.
Then ζmζn \zeta_m\zeta_n is a primitive th\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()\gcd(\cdot) and lcm()\text{lcm}(\cdot) denote the greatest common divisor function and the lowest common multiple function, respectively.


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