Question 108
Compute the sum of the three smallest positive integers $n$ for which
$$
\frac{1+2+3+\cdots+(2024 n-1)+2024 n}{1+2+3+\cdots+(4 n-1)+4 n}
$$
is an integer.
$$
\frac{1+2+3+\cdots+(2024 n-1)+2024 n}{1+2+3+\cdots+(4 n-1)+4 n}
$$
is an integer.