LCM & GCF Calculator
Find the least common multiple and greatest common factor of 2 to 50 whole numbers. Shows the prime factorization of every value and how the GCF and LCM are built from it, with exact arithmetic and clear handling of negatives.
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About the LCM & GCF Calculator
LCM & GCF Calculator finds the least common multiple and the greatest common factor (also called the greatest common divisor or highest common factor) of a list of whole numbers. Enter 2 to 50 values separated by commas, spaces, tabs or new lines.
The tool shows the prime factorization of every value, then builds the GCF from the primes shared by all values at their lowest powers and the LCM from every prime at its highest power. Both results are cross-checked with the Euclidean algorithm, and the LCM is computed with exact BigInt arithmetic so even long results are exact. Negative numbers are treated by their absolute value, because the GCF and LCM are conventionally positive. Zero and decimals are rejected.
How to use
- Type or paste at least two whole numbers, separated by commas, spaces or new lines.
- Press Calculate.
- Read the GCF and LCM, then the prime factorization of each value.
- Follow the working to see how the results were built.
- Copy or download the summary, or press Reset.
Key features
- GCF and LCM of 2 to 50 integers.
- Prime factorization of every value in a table.
- Working that shows the primes and powers used.
- Exact BigInt LCM and a Euclidean cross-check.
- Negative values handled by absolute value, with a note.
- Clear errors for zero, decimals, malformed values and limits.
- Copy and download a plain-text summary.
Best practices
- Do not use thousands separators — commas separate values.
- Use the GCF to simplify fractions and ratios.
- Use the LCM to find a common denominator or a repeating schedule.
- Check that GCF × LCM = a × b holds for two positive numbers.
- Split very long lists into groups if you only need part of the answer.
Benefits
- Shows the method, not just the answer.
- Exact results for long lists and large values.
- Useful for fractions, scheduling and number puzzles.
- Private: runs entirely in your browser.
Frequently asked questions
What is the difference between the GCF and the LCM?
The greatest common factor is the largest whole number that divides every value exactly. The least common multiple is the smallest positive whole number that every value divides into exactly.
How are they found from prime factorizations?
The GCF multiplies the primes shared by all values, each at its lowest power. The LCM multiplies every prime that appears in any value, each at its highest power.
How are negative numbers handled?
They are replaced by their absolute values. −12 has the same factors as 12, and the GCF and LCM are conventionally given as positive numbers. The results note when this happened.
Why is zero not allowed?
Every number divides 0, so it adds nothing to the GCF, and the LCM is not defined when one of the values is 0. Remove zeros from the list.
What are the limits?
Between 2 and 50 values, each a non-zero whole number up to 1,000,000,000,000 in size. Values beyond that are rejected with a message.
Are the results exact?
Yes. Factorization and the GCF use exact whole-number arithmetic within JavaScript’s safe-integer range, and the LCM uses BigInt, so it is exact even when it has hundreds of digits. Both are cross-checked with the Euclidean algorithm.
Can I enter numbers like 1,000?
No — commas are treated as separators, so 1,000 would be read as 1 and 000. Type 1000 instead.
Is anything I enter saved or sent anywhere?
No. Every calculation runs in your browser on your device. Inputs, settings and results are not uploaded and are not saved in browser storage. Reset clears them from the page.