GCD & LCM Calculator
Find Greatest Common Divisor and Least Common Multiple of two integers.
Last reviewed by the myCalculator Editorial Team
Input Parameters
Calculation Results
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Formula & How GCD & LCM Calculator Works
The greatest common divisor (GCD) is the largest whole number that divides both numbers with no remainder, and the lowest common multiple (LCM) is the smallest number that both numbers divide into. For 12 and 18 the divisors of 12 are 1, 2, 3, 4, 6, 12 and of 18 are 1, 2, 3, 6, 9, 18, so the GCD is 6. The LCM follows from LCM = (12 × 18) ÷ GCD = 216 ÷ 6 = 36. The GCD is used to reduce fractions to lowest terms: 12/18 becomes 2/3. The LCM is used to find a common denominator when adding fractions, or to work out when two repeating events, such as a 12-day and an 18-day cycle, next coincide, which is every 36 days.
- Enter First Integer (A): Input your target parameter value.
- Enter Second Integer (B): Input your target parameter value.
- Apply Formula: Calculate using
LCM(A, B) = (|A × B|) / GCD(A, B). - Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)
How is GCD calculated?
Using the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the two numbers until the remainder is zero.
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Authoritative Standards & Verified Reference Citations
Calculations and mathematical logic on this page are grounded in published statutory rules, regulatory standards, and official government data published by the following bodies:
Open government data, scientific datums, and public sector mathematical reference datasets.
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