GCD & LCM Calculator
Free GCD and LCM calculator using the Euclidean algorithm. Find the greatest common divisor and least common multiple with steps.
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Calculate GCD and LCM Instantly
Finding the Greatest Common Divisor (GCD) or Least Common Multiple (LCM) of two numbers is essential for simplifying fractions, solving equations, and many practical applications. Our calculator finds both values instantly using the efficient Euclidean algorithm.
Understanding GCD and LCM
The GCD is the largest number that divides evenly into two or more numbers. The LCM is the smallest number that is a multiple of two or more numbers. These concepts are fundamental in number theory, fractions, and solving real-world problems involving cycles and intervals.
Key Relationship
LCM(a,b) × GCD(a,b) = a × bWhy Use This Calculator?
Dual Calculation
Get both GCD and LCM in a single operation.
Multiple Numbers
Calculate GCD and LCM for two or more numbers simultaneously.
Detailed Steps
See the step-by-step calculation process.
How to Calculate GCD and LCM
Common Applications
Simplifying Fractions
Use GCD to reduce fractions to their lowest terms.
Common Denominators
Use LCM to find the common denominator when adding fractions.
Cycle Problems
Find when cyclical events will coincide.
Group Division
Divide items into equal groups of the largest possible size.
Frequently Asked Questions
GCD is used to simplify fractions to their lowest terms, find common denominators, and solve problems involving equal distribution or grouping.