Question 2
Determine all finite nonempty sets $S$ of positive integers satisfying
$$
\frac{i+j}{(i, j)} \quad \text{is an element of} S \text{ for all } i, j \text{in} S,
$$
where $(i, j)$ is the greatest common divisor of $i$ and $j$.
$$
\frac{i+j}{(i, j)} \quad \text{is an element of} S \text{ for all } i, j \text{in} S,
$$
where $(i, j)$ is the greatest common divisor of $i$ and $j$.