Ah, I think I understand.

Maybe fizzbuzz should use the word “divisible” or “divisor” instead of “multiple”. Compare the explanations for divisor, multiple, and least common multiple.

**Oh, I get it!** http://en.wikipedia.org/wiki/Divisible

In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder.

For example, 7 is a divisor of 42 because 42 / 7 = 6.

**Can you explain that again?** http://en.wikipedia.org/wiki/Multiple_(mathematics)

In mathematics, a multiple is the product of any quantity by an integer. In other words, for the quantity a such as integer, real number, or complex number, b is a multiple of a if b = na for some integer n. The n is also called coefficient or multiplier. Additionally, if a is not zero, this is equivalent to saying that b / a is an integer with no remainder.

Some said the multiple is the product of an integer by another integer so it is called integer multiple. When a and b are both integers, a is also called a factor of b.

**WT… err… Huh?** http://en.wikipedia.org/wiki/Least_common_multiple

A simple algorithm

This method works as easily for finding the LCM of several integers.

Let there be a finite sequence of positive integers X = (x1, x2, …, xn), 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), …, xn(m)), X(1) = X. The purpose of the examination is to pick up the least (perhaps, one of many) element of the sequence X(m). Assuming xk0(m) is the selected element, the sequence X(m+1) is defined as

xk(m+1) = xk(m), k ≠ k0

xk0(m+1) = xk0(m) + xk0.

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). (For a proof and an interactive simulation see reference below, Algorithm for Computing the LCM.)