Let $N\ge 1$. What is the size of the largest $A\subset \{1,\dots ,N\}$ such that $[a,b]\le N$ for all $a,b\in A$, where $[a,b]$ is the least common multiple of $a$ and $b$?Is it attained by choosing all integers in $[1,(N/2{)}^{1/2}]$ together with all even integers in $[(N/2{)}^{1/2},(2N{)}^{1/2}]$?