## Topic outline

• ### Lowest Common Multiple (LCM)

#### Lowest Common Multiple

The Lowest Common Multiple (LCM) of two or more given number is the lowest (or smallest or least) of their common multiples.

Example: LCM of 12 and 15.

Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252…

Multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240

Common Multiples of 12 and 15 are 60, 120, 180, 240…

Lowest Common Multiples of 12 and 15 is 60. (60 is the smallest number that both the numbers are factors of this number.)

#### LCM by Prime Factorization Method

Example: Find LCM of 16, 24 and 56

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

Prime factor of 24 = 2 x 2 x 2 x 3 = 23 x 3

Prime factor of 56 = 2 x 2 x 2 x 7 = 23 x 7

Step2: Identify the maximum number of occurrence of each prime number. Here, 24 (2 has occurred 4 times), 31 (3 has occurred 1 time) and 71 (7 has occurred 1 time)

Step3: Now multiply the outcomes.

2 x 2 x 2 x 2 x 3 x 7 = 336

#### LCM by Division Method

Step 1: Find the prime factors of the two or more numbers by dividing the numbers by least prime number till we get 1. (Choose the least prime that at least divide one of the given numbers)

Step 2: Then multiply all the prime factors to get the LCM.

Example: Find LCM of 20, 25 and 30

LCM of 20, 25 and 30 = 2 x 2 x 3 x 5 x 5 = 300