Question 86
Let $n \geq 2$ be a natural number. For an $n$-element subset $F$ of $\{1, \ldots, 2 n\}$, define $m(F)$ as the minimum of all $\operatorname{lcm}(x, y)$, where $x$ and $y$ are two distinct elements of $F$. Find the maximum value that $m(F)$ can attain.