TH-TMO 2021 Problem 9

Let $S$ be a set of positive integers such that if $a$ and $b$ are elements of $S$ such that $a<b$ , then $b-a$ divides the least common multiple of $a$ and $b$ , and the quotient is an element of $S$ . Prove that the cardinality of $S$ is less than or equal to $2$ .