24 and 36
GCF = 12 and LCM = 72. Prime factorizations are 24 = 2³ × 3 and 36 = 2² × 3².
Find the greatest common factor (also called GCD), least common multiple, prime factorizations, and common factors for two to twenty integers.
The greatest common factor (GCF) is the largest positive integer that divides every input exactly. Greatest common divisor (GCD) is an equivalent term.
The least common multiple (LCM) is the smallest non-negative multiple shared by every input. This calculator reports non-negative results even when inputs are negative.
Repeat until the remainder is zero; the last nonzero divisor is the GCF.
gcd(a, b) = gcd(b, a mod b)Dividing before multiplying preserves exactness and reduces intermediate size.
lcm(a, b) = |(a ÷ gcd(a,b)) × b|This identity applies to two nonzero integers.
GCF(a,b) × LCM(a,b) = |a × b|GCF = 12 and LCM = 72. Prime factorizations are 24 = 2³ × 3 and 36 = 2² × 3².
Pairwise reduction gives GCF = 24 and LCM = 720.
GCF uses the lowest shared prime powers, while LCM uses the highest powers appearing in any input.
GCF and LCM remain exact for BigInt inputs. Prime factors and full factor lists are omitted above 10,000,000,000 to prevent expensive browser work.
Absolute values are used, so outputs are non-negative. GCF(0,n) is |n| and LCM(0,n) is 0. GCF(0,0) is shown as indeterminate because it has no unique greatest divisor.
For 24 = 2³ × 3 and 36 = 2² × 3², the GCF takes 2² × 3 = 12 and the LCM takes 2³ × 3² = 72.
It is the largest positive integer that divides every selected integer without a remainder.
Yes. Greatest common factor and greatest common divisor describe the same value.
It is the smallest non-negative number divisible by every selected integer.
The calculator uses the Euclidean algorithm repeatedly across all inputs.
It divides one value by the GCF before multiplying by the next value.
Yes. This calculator reduces between two and twenty integers pairwise.
GCF(0,n)=|n|, LCM(0,n)=0, and GCF(0,0) is indeterminate.
Yes. Calculations use absolute values and report a non-negative GCF.
Trial division can be expensive, so factorization is not displayed above 10,000,000,000.