The least common multiple of random sets of positive integers

TL;DR

This paper investigates the typical behavior of the least common multiple of random subsets of integers, revealing that for most subsets, the LCM grows exponentially with the size of the set.

Contribution

It provides a probabilistic analysis of the LCM of random subsets, establishing asymptotic behavior for almost all such subsets.

Findings

The LCM of a random subset is approximately exponential in size.

Almost all subsets have an LCM close to 2^{n}.

The study characterizes the typical growth rate of the LCM.

Abstract

We study the typical behavior of the least common multiple of the elements of a random subset $A\subset \{1,\dots, n\}$. For example we prove that $\text{lcm}\{a:\ a\in A\}=2^{n(1+o(1))}$ for almost all subsets $A\subset\{1,\dots,n\}$.