# Table of LCM's vs. table of products

In 2004 Kevin Ford established sharp asymptotics on Erdős' problem on the number of different products $a\cdot b$, $a,b\in \{1,\dots,n\}$.

(http://arxiv.org/abs/math/0401223, see also discussion here: Number of elements in the set $\{1,\cdots,n\}\cdot\{1,\cdots,n\}$)

My naive question is whether there are much less different numbers of the form $\operatorname{lcm}(a,b)$, where $a,b\in \{1,\dots,n\}$.

• I think there'll be about as many numbers of the form lcm$(a,b)$. Ford counts integers having a divisor in an interval $[y,2y]$, and one should be able to adapt this to counting square-free integers with such a divisor. Of course, a square-free integer in the multiplication table arises also as lcm$(a,b)$. – Lucia Aug 14 '15 at 14:55