Any interesting reduction of LCM(a, b) / GCD(a, b)?

Question

I know that $$a\cdot b = \gcd(a, b) \cdot\operatorname{lcm}(a, b)$$

where $a$ and $b$ are positive integers.

I am wondering if there are any other reductions of the following expression:

$$\frac{\operatorname{lcm}(a, b)}{ \gcd(a, b)}$$

Answer 1

Using the formula that you mention you can see that it is equal to the product $$\frac{a}{ \gcd(a, b)}\cdot\frac{b}{ \gcd(a, b)}$$ where the two factors here are coprime. They form the reduced version of the couple $(a,b)$ after you factor out their common divisors.