NMC 2019 Problem 1

A set of different positive integers is called meaningful if for any finite nonempty subset the corresponding arithmetic and geometric means are both integers. $a)$ Does there exist a meaningful set which consists of $2019$ numbers? $b)$ Does there exist an infinite meaningful set? Note: The geometric mean of the non-negative numbers $a_1, a_2,\cdots,$ $a_n$ is defined as $\sqrt[n]{a_1a_2\cdots a_n} .$