GCD & LCM Calculator
Find the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of any set of numbers. Shows step-by-step working. Free, browser-based.
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GCD vs LCM
The GCD (Greatest Common Divisor) is the largest number that divides all given numbers evenly — useful for simplifying fractions. The LCM (Least Common Multiple) is the smallest number divisible by all given numbers — useful for adding fractions with different denominators.
How They Relate
| Property | Formula |
|---|---|
| GCD × LCM = a × b | For two numbers a and b |
| LCM(a,b) | = a × b / GCD(a,b) |
| If GCD = 1 | Numbers are coprime (share no common factors) |
Euclidean Algorithm
The fastest method: repeatedly replace the larger number with the remainder of dividing the larger by the smaller. Stop when the remainder is 0 — the last non-zero remainder is the GCD. This works for any two integers and runs in O(log(min(a,b))) steps.