Question 1
A finite set of distinct positive integers is written on a blackboard. A *move* consists in choosing two numbers and write their lowest common multiple, given that is not already written. The set is called *closed* if no moves are allowed – e.g., the set $\{2, 3, 4, 6\}$ will be closed after number $12$ is added. Determine the maximum number of elements in a closed set given that the initial set contains $10$ numbers.