LCM & HCF Calculator

Find Least Common Multiple and Highest Common Factor with step-by-step solutions

Enter Numbers

Mathematical Operations

Results

Numbers
Input values
12, 18
HCF (GCD)
Highest Common Factor
6
LCM
Least Common Multiple
36

Mathematical Relationship

LCM × HCF = 36 × 6 = 216
Product of numbers = 12 × 18 = 216 ✓

Prime Factorization

Step-by-Step Solution

About LCM

Least Common Multiple (LCM) is the smallest positive integer that is divisible by all given numbers.

Applications:
  • Adding fractions with different denominators
  • Finding common time intervals
  • Solving scheduling problems
  • Pattern repetition calculations

About HCF

Highest Common Factor (HCF) or Greatest Common Divisor (GCD) is the largest positive integer that divides all given numbers.

Applications:
  • Simplifying fractions to lowest terms
  • Dividing objects into equal groups
  • Finding common measurements
  • Cryptography and number theory

Calculation Methods

Prime Factorization

Break numbers into prime factors, then multiply common factors for HCF and all factors for LCM

Division Method

Repeatedly divide by common factors until no common factors remain

Euclidean Algorithm

Use repeated subtraction or division to find HCF, then calculate LCM using the relationship