GCD & LCM Calculator
Fundamental number theory.
GCD & LCM Calculator
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What This Calculator Does
The GCD & LCM Calculator finds the Greatest Common Divisor and Least Common Multiple of two or more integers. GCD is the largest number that divides all given numbers without a remainder.
How It Works
GCD uses the Euclidean algorithm: repeatedly replace the larger number by the remainder of dividing the larger by the smaller. LCM = |a x b| / GCD(a, b).
Example
For 12 and 18: GCD = 6, LCM = (12 x 18) / 6 = 36.
Formula
LCM(a,b) = |a*b| / GCD(a,b)Reading the Results
GCD
The greatest number that divides both A and B evenly.
LCM
The smallest number that is a multiple of both A and B.
Frequently Asked Questions
What is GCD?
The Greatest Common Divisor is the largest positive integer that divides two or more integers without a remainder.
What is LCM used for?
LCM is used when finding common denominators for fractions, scheduling recurring events, and solving gear-ratio problems.
Can GCD work with more than 2 numbers?
Yes. GCD(a,b,c) = GCD(GCD(a,b),c). Apply the algorithm iteratively.