Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Guoyou Qian, Shaofang Hong

Published 2012-04-24, updated 2013-02-24Version 2

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.