Question 19
A basket contains $19$ apples labeled by the numbers $2,3,\ldots,20$, and $19$ bananas labeled by the numbers $2,3,\ldots,20$. Ah Beng picks $m$ apples and $n$ bananas from the basket. However he needs to ensure that for any apple labeled $a$ and any banana labeled $b$ that he picks, $a$ and $b$ are relatively prime. Determine the largest possible value of $mn$.