GCD and LCM

Alice and Bob are playing a game. They have two positive integers $X$ and $Y$. In one operation: - First Alice would replace **exactly one** of the numbers with the [gcd](https://en.wikipedia.org/wiki/Greatest_common_divisor) of current numbers. In words, she would select either $X$ or $Y$ and replace it with $\gcd(X,Y)$. - Then Bob would replace **exactly one** of the numbers with the [lcm](ht