Question 71
Let $n$ be an integer greater than $1$ and let $S$ be the set of $n$-element subsets of the set $\{1, 2, \dots, 2n\}$. Determine
$$
\max_{S \in \mathcal{S}} \min_{x, y \in S, x \neq y} [x, y],
$$
where $[x, y]$ denotes the least common multiple of the integers $x$ and $y$.
$$
\max_{S \in \mathcal{S}} \min_{x, y \in S, x \neq y} [x, y],
$$
where $[x, y]$ denotes the least common multiple of the integers $x$ and $y$.