We arbitrarily take $n$ distinct positive integers $a_{1}, \cdots, a_{n}$, and select a (positive integer) parameter $K$, hoping that the product $K^{n} a_{1} \cdots a_{n}$ of $K a_{1}, \cdots, K a_{n}$ is divisible by the sum of any two terms $K a_{i}+K a_{j}$ $(1 \leqslant i, j \leqslant n, i \neq j)$. Since $n \geqslant 2$, it is clear that taking
$$K=\prod_{1 \leq i<j \leqslant n}\left(a_{i}+a_{j}\right)$$

meets the requirement (note that $K a_{1}, \cdots, K a_{n}$ are distinct).