MathNet 2007-part-01 — 187 problems (EN–VI) Question 155

Let $n$ be a positive integer, set $A \subseteq \{1, 2, \dots, n\}$, and for every $a, b \in A$, $\text{lcm}(a, b) \le n$. Prove that
$$
|A| \le 1.9\sqrt{n} + 5.
$$