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Find the Greatest Common Divisor and Least Common Multiple of two or more numbers — with step-by-step working shown.
GCD & LCM Calculator · Greatest Common Divisor · Least Common Multiple · step-by-step algorithms
Separated by commas. Works for integers of any size.
GCD and LCM are calculated and displayed simultaneously.
The step-by-step method (Euclidean algorithm for GCD, prime factorisation breakdown) is shown so you can follow and verify the calculation.
The Greatest Common Divisor (GCD) — also called the Greatest Common Factor (GCF) or Highest Common Factor (HCF) — is the largest positive integer that divides all the given numbers without a remainder. Example: GCD(48, 36) = 12, because 12 is the largest number that divides both 48 and 36 exactly.
The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all the given numbers. Example: LCM(4, 6) = 12, because 12 is the smallest number that both 4 and 6 divide into exactly. The relationship between GCD and LCM: LCM(a, b) = (a × b) / GCD(a, b).
Simplifying fractions (divide numerator and denominator by their GCD), cryptography (Euclidean algorithm is foundational to RSA encryption), solving problems in number theory, and finding common denominators for fraction arithmetic.
Finding a common denominator when adding or subtracting fractions, scheduling problems (when do two repeating events next coincide), gear ratio calculations, and number theory problems.
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GCD and LCM are fundamental concepts in number theory with direct practical applications — from simplifying fractions to scheduling to cryptography. This calculator finds both values for two or more integers simultaneously, using the Euclidean algorithm for GCD (showing each step) and prime factorisation for LCM (displaying the factor breakdown). The step-by-step working is particularly useful for students verifying their manual calculations or teachers demonstrating the methods, as it shows the reasoning rather than just the answer.
All calculations run in your browser. No data is transmitted to any server.
