The GCF and LCM calculator finds the greatest common factor (GCF) and least common multiple (LCM) for up to 6 numbers using prime factorization, showing every step.
GCF & LCM Calculator
How to Use the GCF & LCM Calculator
The GCF (greatest common factor) and LCM (least common multiple) are foundational concepts for fraction operations and number theory.
Using Prime Factorization
Factor each number into primes. GCF: take the minimum exponent of each shared prime. LCM: take the maximum exponent of all primes. For 12=2²×3 and 18=2×3²: GCF=2¹×3¹=6, LCM=2²×3²=36. Check: GCF×LCM = 6×36 = 216 = 12×18.
Applications
GCF is used to simplify fractions: 18/24 → divide both by GCF(18,24)=6 → 3/4. LCM is used to find common denominators: add 1/12 + 1/18 → LCD=LCM(12,18)=36 → 3/36 + 2/36 = 5/36.
For Multiple Numbers
To find GCF of 3 or more numbers, compute pairwise: GCF(a,b,c) = GCF(GCF(a,b),c). Similarly for LCM. This tool handles up to 6 numbers at once.
FAQ
What is the GCF (greatest common factor)?
The GCF (also called HCF or GCD) is the largest integer that divides all given numbers evenly. GCF(12, 18) = 6 because 6 is the largest number that divides both. Used for simplifying fractions: GCF(8,12)=4, so 8/12 = 2/3.
What is the LCM (least common multiple)?
The LCM is the smallest positive integer divisible by all given numbers. LCM(4, 6) = 12. Used to find common denominators for adding fractions. Relationship: GCF(a,b) × LCM(a,b) = a × b.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
How do you find GCF using prime factorization?
Factor each number into primes. GCF uses the minimum power of each common prime. LCM uses the maximum power of all primes. Example: 12=2²×3, 18=2×3². GCF=2¹×3¹=6. LCM=2²×3²=36.