Lowest Common Multiple (L.C.M)

Lowest Common Multiple (L.C.M)

Definition

The Lowest Common Multiple (LCM) of a group of numbers is the smallest number that is exactly divisible by all the given numbers.

Prime Factorization Method

Example 1: Find LCM of 20, 66, 128

• 20 = 2 × 2 × 5
• 66 = 2 × 3 × 11
• 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

Take highest powers of all prime factors:

LCM = 2⁷ × 3 × 5 × 11 = 42240

Example 2: Find HCF of 78, 128, 196

• 78 = 2 × 3 × 13
• 128 = 2⁷
• 196 = 2 × 2 × 49 = 2² × 7²

Common factor = 2

HCF = 2

Example 3: Find LCM of 84, 92, 76

• 84 = 2 × 2 × 3 × 7
• 92 = 2 × 2 × 23
• 76 = 2 × 2 × 19

LCM = 2² × 3 × 7 × 23 × 19 = 36708

Example 4: Find LCM of 36, 108, 60

• 36 = 2² × 3²
• 108 = 2² × 3³
• 60 = 2² × 3 × 5

LCM = 2² × 3³ × 5 = 540

Important Note

LCM and HCF are used in problems related to fractions, addition, subtraction, and simplification.