GCF & LCM Calculator
Find the Greatest Common Factor (GCF, also called GCD) and Least Common Multiple (LCM) of two or more integers. Handles negative numbers and lists.
Inputs
Two or more integers.
GCF (Greatest Common Factor)
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LCM (Least Common Multiple)
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Prime factors of GCF
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About GCF & LCM Calculator
GCF vs LCM
GCF: largest number that divides all inputs evenly. LCM: smallest number that all inputs divide into evenly. GCF(a,b) × LCM(a,b) = a × b for two numbers.
How it’s calculated
GCF uses the Euclidean algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0; the remaining a is the GCF. LCM is then computed from GCF using the identity above.
Where you use these
Simplifying fractions (divide by GCF). Finding common denominators (LCM). Scheduling repeating events. Cryptographic algorithms (RSA, modular arithmetic).