New lower bounds for the least common multiples of arithmetic progressions.

For relatively prime positive integers u and r, and for 0 ≤ k ≤ n, define u:= u + kr. Let L:= lcm( u, u, ..., u) and let a, l ≥ 2 be any integers. In this paper, the authors show that, for integers α ≥ a, r ≥ max( a, l − 1) and n ≥ lαr, the following inequality holds Particularly, letting l = 3 yields an improvement on the best previous lower bound on L obtained by Hong and Kominers in 2010. [ABSTRACT FROM AUTHOR]