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LCM & GCF Calculator
Least common multiple and greatest common factor.
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GCF
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LCM
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How to use the LCM & GCF Calculator
GCF via Euclid's algorithm; LCM = a×b ÷ GCF.
How LCM and GCF are found
GCF via Euclid's algorithm (repeated remainders — fast even for huge numbers). LCM = a × b ÷ GCF. Example: GCF(12, 18) = 6, so LCM = 12×18÷6 = 36.
Where they're used
LCM gives the smallest common denominator for adding fractions; GCF simplifies them. Both appear constantly in algebra homework, scheduling problems ("when do two cycles align?") and gear-ratio math. See also our fraction calculator.
Frequently Asked Questions
Adding fractions with different denominators — the LCM is the smallest common denominator.