What are HCF and LCM? How are they calculated?

HCF (Highest Common Factor) and LCM (Least Common Multiple) are mathematical concepts used to find common factors and multiples of numbers.

1. HCF (Highest Common Factor)

Definition

HCF is the largest number that divides two or more numbers exactly.

Example

Find HCF of 12 and 18:

Factors of 12 → 1, 2, 3, 4, 6, 12
Factors of 18 → 1, 2, 3, 6, 9, 18

Common factors → 1, 2, 3, 6
HCF = 6

2. LCM (Least Common Multiple)

Definition

LCM is the smallest number that is a multiple of two or more numbers.

Example

Find LCM of 12 and 18:

Multiples of 12 → 12, 24, 36, 48...
Multiples of 18 → 18, 36, 54...

LCM = 36

Methods to Calculate HCF and LCM

1. Prime Factorization Method

• Break numbers into prime factors
• HCF → take common factors with lowest powers
• LCM → take all factors with highest powers

2. Division Method

• Divide numbers step by step
• Used for larger numbers

Important Formula

HCF × LCM = Product of the two numbers

Example:
12 × 18 = 216
HCF × LCM = 6 × 36 = 216

Summary

• HCF → greatest common divisor
• LCM → smallest common multiple
• Both are important for solving mathematical problems