Math Doubts

Least Common Multiple


A small number that appears commonly in the multiples of two or more numbers is called the least common multiple.


At least one or more commonly appearing multiplies can be identified when the multiplies of two or more numbers are compared. The first multiple is a small number in the list of common multiples of them and it is called the least common multiple.

The least common multiple is also called alternatively as follows in mathematics.

  1. Lowest common multiple
  2. Smallest common multiple

The smallest or least or lowest common multiple is popularly called by its short form L.C.M in mathematics.

least or lowest or smallest common multiple lcm

Now, let’s understand the concept of the LCM from an example.

Firstly, let’s write the multiples of two, multiples of three and multiples of four.

$M_2$ $\,=\,$ $2,$ $4,$ $6,$ $8,$ $10,$ $\color{blue}{12},$ $14,$ $16,$ $18,$ $20,$ $22,$ $\color{blue}{24},$ $26,$ $28,$ $30,$ $32,$ $34,$ $\color{blue}{36},$ $\cdots$

$M_3$ $\,=\,$ $3,$ $6,$ $9,$ $\color{blue}{12},$ $15,$ $18,$ $21,$ $\color{blue}{24},$ $27,$ $30,$ $33,$ $\color{blue}{36},$ $\cdots$

$M_4$ $\,=\,$ $4,$ $8,$ $\color{blue}{12},$ $16,$ $20,$ $\color{blue}{24},$ $28,$ $32,$ $\color{blue}{36},$ $\cdots$

Now, compare the multiples of numbers $2,$ $3$ and $4$. We can recognize that there are some multiples commonly appeared like $12,$ $24,$ $36$ and so on.

The number $12$ is a small number in the list of commonly appearing multiplies of $2,$ $3$ and $4$. So, the number $12$ is called the LCM of numbers $2,$ $3$ and $4$.


There are three methods to find the LCM in mathematics.

  1. Common multiple method
  2. Prime factor method
  3. Common division method

Let’s learn each method with understandable steps to know how to find the smallest common multiple.


The questions on finding the LCM of two or more numbers for your practice with examples and solutions to learn how to find the L.C.M of two or more numbers.

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved