GCF & LCM Calculator

How to Use This Calculator

Enter two numbers in the input boxes and press Calculate. The tool finds both the GCF and LCM instantly. You also see the prime factorization of each number, which shows exactly how the answer was reached. This is helpful for checking your own work.

GCF vs LCM

The GCF (Greatest Common Factor) is the largest number that divides evenly into both numbers. Use the GCF when you want to simplify a fraction or split something into equal groups as large as possible.

The LCM (Least Common Multiple) is the smallest number that both numbers divide into evenly. Use the LCM when you need a common denominator for fractions, or when you need to find when two repeating events will happen at the same time again.

Finding GCF Using Prime Factorization

To find GCF(24, 36) step by step:

1. Factor 24 into primes: 2 x 2 x 2 x 3
2. Factor 36 into primes: 2 x 2 x 3 x 3
3. Find the shared prime factors: 2 x 2 x 3
4. Multiply them together: 2 x 2 x 3 = 12

GCF(24, 36) = 12

Finding LCM

The fastest way uses the GCF. Once you have the GCF, you can find the LCM with: LCM = (a x b) / GCF. For 24 and 36: LCM = (24 x 36) / 12 = 864 / 12 = 72. You can check: 72 / 24 = 3 (whole number) and 72 / 36 = 2 (whole number). Both pass, so 72 is correct.

Reference Table: Common Pairs

Common Mistakes to Avoid

• Confusing GCF and LCM. GCF is always smaller than or equal to both numbers. LCM is always larger than or equal to both numbers.
• Finding a common factor that is not the greatest. Keep looking to make sure you have found the largest one.
• Forgetting that GCF x LCM = a x b. This formula is a quick way to check your answer.
• Using GCF when you need LCM for fraction denominators. These tasks need different tools.