Least Common Multiple (LCM)
Definition

In general, the least common multiple (lcm) is the smallest multiple that a set of terms have in common.


Example 1: 36x7 is the least common multiple of 12x7 and 18x3.


Example 2: 36x5y4z is the least common multiple of 12x5y2z, 6x4y3z and 18x3y4.


Example 3: 360x50y4z is a common multiple of 12x5y2z, 6x4y3z and 18x3y4, but it is NOT the LEAST common multiple.


Example 4: 12x50y2z is a NOT a COMMON multiple of 12x5y2z, 6x4y3z and 18x3y4. It is therefore not the LEAST common multiple.


Example 5: 7xy is NOT a multiple of 12x5y2z, 6x4y3z or 18x3y4. It is therefore not the least common multiple.



Definition (Natural Numbers)

The least common multiple (lcm) is the smallest natural number that is a multiple of two or more given natural numbers.


Example 1: 36 is the least common multiple of 12 and 18.


Example 2: 360 is a common multiple of 12 and 18, but it is NOT the LEAST common multiple.


Example 3: 24 is NOT a COMMON multiple of 12 and 18. It is therefore not the GREATEST common multiple.


Example 4: 20 is NOT a multiple of 12 or 18. It is therefore not the greatest common multiple.



Demonstration Applet (Natural Numbers)
Image only

Instructions text as in global.js

Your browser does not support the canvas element.