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GCD & LCM Calculator

Find the GCD and LCM of two or more numbers.

Results

GCD (HCF)12
LCM72
Product (a × b)864
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What is GCD & LCM?

GCD (Greatest Common Divisor) is the largest number that divides both numbers evenly. LCM (Least Common Multiple) is the smallest number that both numbers divide into evenly.

GCD is also called HCF (Highest Common Factor). These are fundamental concepts used in simplifying fractions, solving equations, and number theory.

Formula

GCD uses the Euclidean algorithm: GCD(a, b) = GCD(b, a mod b) until b = 0

LCM = (a × b) / GCD(a, b)

Example: GCD(24, 36) 36 = 1×24 + 12 24 = 2×12 + 0 GCD = 12 LCM = (24×36)/12 = 72

How to use this GCD & LCM Calculator?

1. Enter two numbers. 2. See the GCD and LCM instantly. 3. Use GCD to simplify fractions (e.g., 24/36 = 2/3).

Frequently asked questions

What is the relationship between GCD and LCM?
GCD(a,b) × LCM(a,b) = a × b. This means if you know GCD, you can find LCM and vice versa.
What is GCD of two prime numbers?
The GCD of any two different prime numbers is always 1. They are co-prime.
Where is LCM used in real life?
Finding when two events with different intervals coincide (e.g., two buses with different schedules), adding fractions with different denominators.
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