Question 39
There are two blackboards $A$ and $B$, and on each of these blackboards certain number of distinct integers greater than or equal to $2$ and less than or equal to $20$ are written in such a way that any pair of numbers one of which is chosen from $A$ and the other from $B$ are relatively prime. Determine the maximum possible value the product of the number of integers written on $A$ and the number of integers written on $B$ can take.