Factors, GCF & LCM Calculator
List every factor of your numbers and find their greatest common factor (GCD) and least common multiple (LCM).
Enter two or more integers to see the complete list of factors for each one, then get their greatest common divisor (GCD) and least common multiple (LCM) — with the math steps shown, not just the answer.
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How to use
- Enter two or more whole numbers, separated by commas or spaces.
- Review every factor of each number along with the prime factorization table showing the shared factors.
- Read the final GCD and LCM results and copy them.
FAQ
- What is the Euclidean algorithm?
- It's the fastest and best-known method for finding a greatest common divisor. Given two natural numbers A and B, divide A by B and take the remainder R: the GCD of B and R is the same as the GCD of A and B. Repeat that step until the remainder is zero, and the answer falls out.
- Is there a relationship between the GCD and LCM of two numbers?
- Yes — for any two natural numbers A and B, 'GCD(A, B) × LCM(A, B) = A × B' always holds. For example, 12 and 18 have a GCD of 6 and an LCM of 36, and both 6 × 36 and 12 × 18 come out to exactly 216. This means once you know the GCD, you can find the LCM with a single division instead of computing it separately.
- Is there a relationship between the GCD and LCM of two numbers?
- Yes — for any two natural numbers A and B, 'GCD(A, B) × LCM(A, B) = A × B' always holds. For example, 12 and 18 have a GCD of 6 and an LCM of 36, and both 6 × 36 and 12 × 18 come out to exactly 216. This means once you know the GCD, you can find the LCM with a single division instead of computing it separately.