The Lowest Common Multiple (LCM)

The Lowest Common Multiple (LCM)

A multiple is a number which can be divided by another number without leaving a remainder. Multiplication is the opposite of division. Therefore, a multiple is a product obtained after multiplying two or more numbers. The LCM is the least number which can be divided by two or more numbers without leaving a remainder.

The Lowest Common Multiple (LCM) of three numbers

The Lowest Common Multiple (LCM) of three numbers is the least number which can be divided by the three given numbers. There are several methods of finding the LCM of numbers as shown in the following examples:

Find the L.C.M of 2, 4 and 6.

Solution

By listing all multiples of the given numbers

List all multiples of 2, 4 and 6

Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, …

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, …

Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, …

Common multiples of 2, 4 and 6 are 12, 24, 36, … The multiples of given three numbers are infinite.

Therefore, the LCM of 2, 4 and 6 is 12.

Example

Find the LCM of 2, 4 and 12.

Solution

Finding the LCM by prime factors method

The Lowest Common Multiple is a product of 2, 2 and 3.

Thus, LCM = 2 × 2 × 3 = 12

Therefore, LCM of 2, 4 and 12 is 12.