Question 47
A sequence of positive integers $a_{1}, a_{2}, \ldots$ is such that for each $m$ and $n$ the following holds: if $m$ is a divisor of $n$ and $m\lt n$, then $a_{m}$ is a divisor of $a_{n}$ and $a_{m}\lt a_{n}$. Find the least possible value of $a_{2000}$.