- Enter 2 or more positive integers separated by commas or spaces. Example: 12, 18, 24. Negative numbers and decimals are not supported since GCF/LCM apply to whole numbers.
- Read the GCF. The Greatest Common Factor is the largest number that divides all your inputs evenly. GCF(12, 18, 24) = 6. It simplifies fractions and factors algebraic expressions.
- Read the LCM. The Least Common Multiple is the smallest number that is divisible by all your inputs. LCM(4, 6) = 12. It gives the common denominator for adding fractions.
- Check prime factorizations. The calculator shows how each number breaks down into prime factors, which is the underlying method used for both calculations.
GCF and LCM Calculator
Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of two or more numbers.
Enter 2 or more positive integers
Prime Factorizations
12= 2^2 x 3
18= 2 x 3^2
24= 2^3 x 3
GCF (GCD)
6
Greatest Common Factor
LCM
72
Least Common Multiple
LCM(12, 18, 24) = 72
How to Use the GCF and LCM Calculator
GCF and LCM Methods
Euclidean algorithm for GCF: GCF(48, 18): 48 = 2 × 18 + 12 18 = 1 × 12 + 6 12 = 2 × 6 + 0 → GCF = 6 LCM from GCF: LCM(a, b) = (a × b) / GCF(a, b) LCM(12, 18) = (12 × 18) / 6 = 216/6 = 36 Prime factorization method: 12 = 2² × 3 18 = 2 × 3² GCF = 2¹ × 3¹ = 6 (lowest powers) LCM = 2² × 3² = 36 (highest powers)
Key identity: GCF(a, b) × LCM(a, b) = a × b. This lets you find LCM quickly once you know GCF: LCM = (a × b) / GCF.
Frequently Asked Questions
The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD) or Highest Common Factor (HCF), is the largest number that divides two or more integers without a remainder. GCF(24, 36) = 12 because 12 divides both. Main uses: simplifying fractions (12/18 → divide both by GCF 6 → 2/3), factoring polynomials in algebra, and reducing ratios to simplest form. In carpentry, GCF tells you the largest equal-sized tiles that will fit a room without cutting.