Question 84
Each of the positive integers $a_{1}, a_{2}, \ldots, a_{n}$ is less than $2016$, and the least common multiple of any two is greater than $2016$. Show that
$$
\frac{1}{a_{1}}+\cdots+\frac{1}{a_{n}}\lt 1+\frac{n}{2016}.
$$
$$
\frac{1}{a_{1}}+\cdots+\frac{1}{a_{n}}\lt 1+\frac{n}{2016}.
$$