GCF and LCM Calculator

Two numbers carry an entire fraction curriculum: the greatest common factor and the least common multiple. The GCF simplifies fractions and ratios; the LCM is the common denominator that makes addition and comparison possible. Finding them by listing factors works for small numbers and collapses into chaos for larger ones - the same four numbers turn into an error-prone slog.

GCF and LCM Calculator takes two to five numbers and returns both answers instantly and exactly. Every number is reduced to its prime factorization, which is displayed step by step, and the GCF and LCM are assembled from those primes by the smallest and largest exponent rules. The classic identity GCF x LCM = a x b is included as a built-in check. It is the fastest route from four numbers to a correct, verifiable answer.

• Two to five numbers: The whole set handled at once.
• Both answers: GCF and LCM side by side.
• Prime factorization shown: Every step visible and verifiable.
• Built-in identity check: GCF x LCM = a x b confirmed for pairs.
• Exact by construction: Integer arithmetic only, no rounding.
• Live computation: Results update as you type.
• Copy or download: Results ready for homework and notes.
• Free and private: Everything runs in your browser; nothing is uploaded.

1. Enter the numbers - two to five integers, one per field.
2. Watch the results appear as you type - no button to press.
3. Read the GCF and the LCM for the whole set.
4. Check the prime factorizations to see exactly how each answer was built.
5. Verify with the identity when two numbers are entered.
6. Copy or download the result for your work.

Example 1 - Simplifying 12/18. Enter 12 and 18: the GCF is 6, so 12/18 = 2/3 after dividing by it. The prime factorizations 2^2 x 3 and 2 x 3^2 make the shared factors visible.

Example 2 - Adding 1/4 + 1/6. Enter 4 and 6: the LCM is 12, the lowest common denominator. The sum is 3/12 + 2/12 = 5/12.

Example 3 - Three numbers. Enter 6, 8, 12: the GCF is 2 and the LCM is 24 - the tool shows how the three factorizations combine.

Example 4 - Scheduling. A bus comes every 8 minutes and a train every 12: they align every LCM(8,12) = 24 minutes.

Example 5 - The identity check. Enter 15 and 20: GCF 5, LCM 60, and 5 x 60 = 300 = 15 x 20, confirmed in the output.

• Both key answers: GCF and LCM in one view.
• Verifiable steps: Prime factorizations shown, not hidden.
• Faster than factoring by hand: Four and five numbers included.
• Built-in cross-check: The classic identity confirmed for pairs.
• Exact results: Pure integer arithmetic, no rounding.
• Free and private: Runs entirely in the browser with nothing uploaded.