Question 29
How many pairs of positive integers $x, y$ are there, with $x \leq y$, and such that $\operatorname{gcd}(x, y)=5!$ and $\operatorname{lcm}(x, y)=50!$.
Note. $\operatorname{gcd}(x, y)$ denotes the greatest common divisor of $x$ and $y$, $\operatorname{lcm}(x, y)$ denotes the least common multiple of $x$ and $y$, and $n!=n \times(n-1) \times \cdots \times 2 \times 1$.
Note. $\operatorname{gcd}(x, y)$ denotes the greatest common divisor of $x$ and $y$, $\operatorname{lcm}(x, y)$ denotes the least common multiple of $x$ and $y$, and $n!=n \times(n-1) \times \cdots \times 2 \times 1$.