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GCD and LCM Calculator - Greatest Common Divisor
Free GCD and LCM calculator. Find the Greatest Common Divisor (GCD/HCF) and Least Common Multiple (LCM) of two or more numbers instantly.
GCD & LCM Calculator
Find Greatest Common Divisor and Least Common Multiple
Results
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and click the "Calculate" button
GCD and LCM Explained
GCD (Greatest Common Divisor), also called HCF (Highest Common Factor), is the largest number that divides two or more numbers without a remainder. LCM (Least Common Multiple) is the smallest number that is a multiple of all given numbers. These are fundamental concepts in number theory and fraction operations.
How to Use This Calculator
- Enter two or more whole numbers separated by commas
- Click Calculate
- View GCD, LCM, and prime factorization
GCD and LCM Relationship
GCD(a,b) × LCM(a,b) = a × b
For two numbers, LCM = (a × b) / GCD(a,b). GCD is found using the Euclidean algorithm.
Frequently Asked Questions
What's the difference between GCD and LCM?
GCD is the largest number that divides all inputs evenly. LCM is the smallest number that all inputs divide into evenly. Example: GCD(12,18)=6, LCM(12,18)=36.
When is GCD useful?
GCD is used to simplify fractions, find common denominators, solve problems involving equal-sized groups, and in cryptography (RSA algorithm).
When is LCM useful?
LCM helps find when events coincide (schedules), add fractions with different denominators, and solve problems involving repeating cycles.
What is the Euclidean algorithm?
It's an efficient method to find GCD: divide larger by smaller, then divide divisor by remainder, repeat until remainder is 0. The last non-zero remainder is the GCD.
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