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1. CMB 2014 (vol 57 pp. 551)

Kane, Daniel M.; Kominers, Scott Duke
Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
For relatively prime positive integers $u_0$ and $r$, we consider the least common multiple $L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n)$ of the finite arithmetic progression $\{u_k:=u_0+kr\}_{k=0}^n$. We derive new lower bounds on $L_n$ that improve upon those obtained previously when either $u_0$ or $n$ is large. When $r$ is prime, our best bound is sharp up to a factor of $n+1$ for $u_0$ properly chosen, and is also nearly sharp as $n\to\infty$.

Keywords:least common multiple, arithmetic progression

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