MathNet 2010 — Part 04 Question 118

Given are $m$ positive integers such that $1 \le a_1 \le a_2 \le \dots \le a_m \le 400$. Show that $m \le 40$, if $\text{gcd}(a_i, a_j) \le 400$ for all $i$ and $j$ ($1 \le i, j \le m$).