GCD & LCM Calculator
Find the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two numbers simultaneously.
GCD (Greatest Common Divisor)
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LCM (Least Common Multiple)
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Quick Examples
Understanding GCD and LCM
Greatest Common Divisor (GCD)
The GCD of two or more integers is the largest positive integer that divides each of them without a remainder.
GCD(a, b) = the largest number that divides both a and b
Least Common Multiple (LCM)
The LCM of two or more integers is the smallest positive integer that is divisible by each of them.
LCM(a, b) = the smallest number that both a and b divide into
The Fundamental Relationship
GCD(a, b) × LCM(a, b) = a × b
Examples
| Numbers | GCD | LCM |
|---|---|---|
| 12, 18 | 6 | 36 |
| 24, 36 | 12 | 72 |
| 15, 25 | 5 | 75 |
| 8, 12 | 4 | 24 |
| 7, 11 | 1 | 77 |
Frequently Asked Questions
What is GCD and why is it useful?
GCD (Greatest Common Divisor) is the largest number that divides two or more numbers evenly. It's essential for simplifying fractions to lowest terms.
What if GCD equals 1?
When GCD(a, b) = 1, the numbers are called "relatively prime" or "coprime." This means they share no common factors other than 1.