Resolution of an Erdős' problem on least common multiples

Abstract

Erdős posed the question whether there exist infinitely many sets of consecutive numbers whose least common multiple (lcm) exceeds the lcm of another, larger set with greater consecutive numbers. In this paper, we answer this question affirmatively by proving that the ratio of the lcm's can be made arbitrarily large.

arXiv comment5 Pages. Comments appreciated, especially on the sieves-like question (Question 3)