GCD & LCM Calculator
What is a GCD & LCM Calculator?
Calculate the Greatest Common Divisor (GCD / HCF) and Least Common Multiple (LCM) for two or more integer numbers. Includes step-by-step Euclidean algorithm work.
Why Use This Tool?
- Math Homework & Education: Verify Greatest Common Factor (GCF) and LCM calculations.
- Fraction Operations: Find Least Common Denominator (LCD) to add or subtract fractions.
- Gear & Cycle Math: Compute repeating alignment cycles for gears or scheduled tasks.
How to Use
- Enter two or more positive integers separated by commas (e.g. `24, 36, 60`).
- Click Calculate to view GCD (HCF) and LCM.
- Inspect step-by-step Euclidean division algorithm work.
Real Working Example
Input:
Numbers: 24, 36, 60
Output Result:
GCD (HCF): 12 | LCM: 360
Important Technical Details & Formulas
- Euclidean Division Algorithm: Computes `GCD(a, b) = GCD(b, a mod b)` recursively.
- LCM Math Formula: `LCM(a, b) = (|a * b|) / GCD(a, b)`.
- Client-Side Engine: Fast calculations in browser memory.
Related Mathematics & Financial Tools
- Prime Factorization Calculator: Factorize numbers into prime factors.
- Fraction Calculator: Calculate and simplify fractions.
- Ratio Calculator: Simplify ratios.
Frequently Asked Questions
What is the difference between GCD and LCM?
GCD (Greatest Common Divisor) is the largest number that divides into all numbers without a remainder; LCM (Least Common Multiple) is the smallest positive number that is a multiple of all numbers.
Is HCF the same as GCD?
Yes, Highest Common Factor (HCF) and Greatest Common Divisor (GCD) are identical mathematical terms.
How does the Euclidean algorithm find GCD?
It repeatedly computes remainders (a mod b) until the remainder reaches 0.
Is it free?
Yes, 100% free.
Can I calculate GCD for more than two numbers?
Yes, enter any series of comma-separated numbers (e.g. 12, 18, 30, 42).