On the distribution of lcm of k-tuples and related problems

TL;DR

This paper investigates the distribution of the least common multiple of k-tuples of positive integers within a range, refining previous results and making progress on an existing conjecture in number theory.

Contribution

It refines earlier results on the distribution of the LCM of k-tuples and provides partial progress towards a conjecture related to this topic.

Findings

Refined bounds on the distribution of LCM of k-tuples

Partial verification of a conjecture by Hilberdink, Luca, and Tóth

Improved understanding of related number-theoretic problems

Abstract

We study the distribution of the least common multiple of positive integers in N\cap [1, x] and related problems. We refine some results of Hilberdink and T\'{o}th (2016). We also give a partial result toward a conjecture of Hilberdink, Luca, and T\'{o}th (2020).