  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 $a$.
