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Let u0, r, α and n be positive integers such that (u 0, r) = 1. Let uk = u0 + kr for 1 ≤ k ≤ n. We prove that Ln := lcm{u0, u1, ⋯ , un} ≥ u0rα(r + 1)nif n < rα. This improves the lower bound of Ln obtained previously by Farhi, Hong and Feng. © 2008 American Mathematical Society.

Improvements of lower bounds for the least common multiple of finite arithmetic progressions