Least Common Multiple

Definition

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

Introduction

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.

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 $4$.

Methods

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.

Worksheet

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.