Number & Math
GCD / LCM Calculator
Greatest common divisor, least common multiple, prime check and factorisation.
Numbers (comma- or space-separated)
3 valid number(s).
GCD
6
LCM
72
About this tool
Type two or more integers and see their GCD (greatest common divisor), LCM (least common multiple) and the prime factorisation of each. Single-number mode runs a primality test and lists all factors. Handles arbitrary precision via BigInt, so 50-digit numbers work.
FAQs
What's the difference between GCD and LCM?
GCD is the largest number that divides every input - useful for reducing fractions. LCM is the smallest number divisible by every input - useful for synchronising periodic events or adding fractions.
How big can the inputs be?
Practically unlimited - the tool uses BigInt. Very large numbers slow primality testing into the seconds range; factoring a 50-digit semiprime can take much longer (that's RSA territory).
Which primality test is used?
Miller-Rabin with deterministic witnesses for numbers up to 3 * 10^18, falling back to probabilistic Miller-Rabin (20 rounds) for larger inputs. False-positive probability under 1 / 4^20.
How does factorisation work?
Trial division by small primes first, then Pollard-Rho for larger composite factors. Numbers with very large prime factors (50+ digits) can stall - those are the cases RSA was designed around.
Why is GCD(0, n) = n?
By definition, the GCD of 0 and n is n - every number divides 0. The Euclidean algorithm relies on this base case to terminate.