The applet below illustrates an algorithm for finding the Least Common Multiple (LCM) of a number of integers.

Let there be a finite sequence of positive integers X = (x₁, x₂, ..., x_n), n > 1. The algorithm proceeds in steps as follows: on each step m it examines and updates the sequence X^(m) = (x₁^(m), x₂^(m), ..., x_n^(m)), X⁽¹⁾ = X. The purpose of the examination is to pick the least (perhaps, one of many) element of the sequence X^(m). Assuming x_k0^(m) is the selected element, the sequence X^(m+1) is defined as

In other words, the least element is increased by the corresponding x whereas the rest of the elements pass from X^(m) to X^(m+1) unchanged.

The algorithm stops when all elements in sequence X^(m) are equal. Their common value L is exactly LCM(X).

(In the applet the numbers x₁, x₂, ..., x_n that appear at the top row are modifiable by clicking left or right off their vertical center line. Press button Compute to see the algorithm running. The blue numbers the ones that have been modified at one of the steps.)