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LCM & HCF / GCD Calculator

Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD / HCF) of two or more numbers using Euclidean and prime factorization methods.

How to Use LCM & HCF / GCD Calculator

  1. Enter Numbers: Enter any two or more numbers separated by commas or spaces.
  2. Click Calculate: Get instant result of LCM and HCF / GCD.
  3. Study Methods: Check the Prime factorization and Euclidean Division method steps.

Explanation & How It Works

HCF / GCD (Greatest Common Divisor): The greatest integer that is completely divisible by each of the numbers.

LCM (Least Common Multiple): The least positive integer that is divisible by all the numbers.

Calculation Formula & Rules

For any two positive integers $a$ and $b$:

LCM(a, b) × GCD(a, b) = a × b
LCM(a, b) = (a × b) / GCD(a, b)

Example Calculation

Example: Find LCM and GCD of 24 and 36.

  • Prime factors of 24: 2³ × 3¹
  • Prime factors of 36: 2² × 3²
  • GCD: Lowest common powers = 2² × 3¹ = 12.
  • LCM: Highest powers = 2³ × 3² = 72.

Practical Uses for LCM and GCD

  • LCM: Planning periodic activities, creating periodic traffic signals, organizing planets’ orbit, adding fractions with different denominators.
  • GCD: Cutting material into squares to minimize leftover material, reducing fractions, distributing things equally among gift packages.

Frequently Asked Questions

What is the Euclidean Algorithm? ▼
An efficient method for computing the GCD of two numbers by repeatedly dividing the larger number by the remainder until the remainder is zero.