Is there a commonly used term for a number divided by its greatest common divisor?

Question

Does the expression $\frac{a}{\gcd(a, b)}$ have a common name?

This type of expression occurs frequently in a program I'm writing. Since $ \forall a,b \in \mathbb{N^{*}}: \frac{a}{\gcd(a, b)} \perp \frac{b}{\gcd(a, b)}$, I've been calling this the coprime part or coprime residue of $a$ relative to $b$. I'd prefer to use a term of art if one exists.

Answer 1

Perhaps you were looking for additive order.

Let $a\in\mathbb{Z}_n$. Then, the smallest positive solution of the congruence $ax\equiv0\pmod{n}$ is called additive order of $a$, which is given by ${n\over gcd(a,n)}$.