Least Common Multiple (LCM)

Multiples

Product of two given numbers is called multiples. Multiple is the result of multiplying any number with other numbers like 1, 2, 3, 4 etc.

Example:

Multiple of 2 - 2, 4, 6, 8, 10, 12 and so on

Multiple of 3 – 3, 6, 9, 12, 15, 18, 21, and so on

Common Multiples

Common multiple means a number that is multiple of two or more numbers.

Example:

Multiple of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ….

Multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 …..

Common multiple of 2 and 3 are 6, 12, 18 …..

Least Common Multiples

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

Example: Find LCM of 12 and 18

Multiples of 12 are 12, 24, 36, 48, 60, 72, 84…

Multiples of 18 are 18, 36, 54, 72, 90, 108…..

Common Multiples of 12 and 18 are 36, 72…

Least Common Multiples of 12 and 18 is 36, 72

LCM by Prime Factorization Method

Example: Find LCM of 36 and 64

Step1: Find out the prime factors of the given numbers.

Prime factor of 36 = 2 x 2 x 3 x 3 = 2² x 3²

Prime factor of 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2⁶

Step2: Identify the maximum number of occurrence of each prime number.

Here, 2⁶ (2 has occurred 6 times) and 3² (3 has occurred 2 times)

Step3: Now multiply the outcomes.

2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576

LCM by Division Method

Find the prime factors of the two or more numbers by dividing the numbers till we get 1 and then multiply all the prime factors to get the LCM.

Example: Find LCM of 4, 6 and 8

LCM of 4, 6 and 8 = 2 x 2 x 2 x 3 = 24