Compute greatest common divisor and least common multiple for two integers.
Updated
GCD: 12
LCM: 72
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In-depth guide
The greatest common divisor (GCD) is the largest integer that divides two numbers exactly; the least common multiple (LCM) is the smallest number both divide into. This tool computes both for a pair of integers instantly in your browser.
GCD is found with the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the two, until the remainder is zero — the last non-zero value is the GCD. LCM is then derived cheaply from it: LCM(a, b) = |a × b| ÷ GCD(a, b). This avoids factorising the numbers, which is why it stays fast even for large inputs.
GCD reduces a fraction to lowest terms by dividing numerator and denominator by it. LCM finds a common denominator for adding fractions, and answers "when do two repeating cycles line up again?" — from gear ratios to scheduling jobs that run every few hours. Both also underpin modular arithmetic in cryptography.
Everything is calculated locally in your browser — the numbers you enter are never uploaded. Note GCD(0, 0) is undefined, since every integer divides zero.
Use this calculator for quick everyday estimates, date math, percentages, bill splitting, or simple planning. Use an official source or domain-specific calculator when legal, billing, payroll, or compliance accuracy is required.
The greatest common divisor is the largest integer that divides both numbers exactly.
The least common multiple is the smallest positive number that both inputs divide into.
Yes. Their absolute values are used for the calculation, since divisibility ignores sign.
Via the Euclidean algorithm — repeatedly replacing the larger number with the remainder of dividing the two until the remainder is zero.
LCM(a, b) equals the absolute value of a times b, divided by GCD(a, b). This avoids factorising the numbers.
GCD(0, n) is n, but GCD(0, 0) is undefined because every integer divides zero.
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