Finding the LCM by Common Multiple Method

The common multiple method is a most useful mathematical approach to find the least common multiple of two or more given numbers. In this method, a lowest common multiple is identified from the list of multiples of the all given numbers and it is taken as the required LCM of the given numbers.

Procedure

There are three simple steps involved in common multiple method for finding the lowest common multiple (L.C.M) of the given two or more numbers.

Write a few multiples of each number.
Identify the common multiples from the list of multiples of the numbers.
Take the lowest common multiple as the required least common multiple of the numbers.

Example

$2$, $3$ and $4$ are three given numbers. Let’s learn how to find the LCM of these three numbers by the common multiple method. Firstly, write a few multiples of each number in a row. The multiples of $2$, $3$ and $4$ are denoted by $M_2$, $M_3$ and $M_4$ respectively.

$M_2$ $\,=\,$ $2, 4, 6, 8, 10, 12, 14, \ldots$

$M_3$ $\,=\,$ $3, 6, 9, 12, 15, 18, 21, \ldots$

$M_4$ $\,=\,$ $4, 8, 12, 16, 28, 32, 36, \ldots$

Now, compare each multiple of $2$ with the multiples of $3$ and $4$.

The number $6$ is a multiple of $2$ and $3$ but there is no multiple $6$ in the multiples of $4$. So, forget about the multiple $6$ and then continue the process of comparing the multiples of them for a common multiple.

The number $12$ is a common multiple of $2$, $3$, and $4$. You can get more common multiples of $2$, $3$ and $4$ if you write more multiples of each of the given number. However, the common multiple $12$ is a smallest number. Therefore, the common multiple $12$ is called the lowest or least common multiple of the given numbers $2$, $3$ and $4$.

The LCM of the given numbers $2$, $3$ and $4$ is $12$.

Thus, the common multiple method is used to find the least common multiple of the given two or more numbers in mathematics.