Divisible by Every Common Divisor of $a$ and $b$

Number Theory Level 4

Find the number of pairs of positive integers $(a,b)$ with $1\leq a < b \leq 100$ such that

there is at least one positive integer $m$ with $a<m<b$ such that $m$ is divisible by every common divisor of $a$ and $b.$

Divisible by Every Common Divisor of aaa and bbb