Arithmetic
LCM & GCF Calculator
List any collection of integers to instantly see their greatest common factor (GCF) and least common multiple (LCM).
Feed any list of integers to get the greatest common factor and least common multiple.
Fundamental relationships
LCM(a, b) = |ab| ÷ GCD(a, b)
The calculator cleans the input list, computes the greatest common divisor across all numbers, then leverages the gcd-derived formula to produce the LCM.
How to use
- Type integers separated by commas, spaces, or new lines.
- The tool removes zeros, computes the GCF, and derives the LCM.
- Review the count of numbers processed to verify your input.
Example
Input: Numbers = 24, 60, 90
Output: Greatest common factor = 6, Least common multiple = 360
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for LCM & GCF Calculator: lcm and gcf calculator, lcm calculator, gcf calculator, greatest common factor calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
LCM & GCF Calculator: Simultaneously get least common multiple and greatest common factor. It's built around lcm, gcf, divisibility, so you can go from a raw question to a checked answer without switching tools.
The math behind it: The calculator cleans the input list, computes the greatest common divisor across all numbers, then leverages the gcd-derived formula to produce the LCM. The core relationship is LCM(a, b) = |ab| ÷ GCD(a, b), shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Type integers separated by commas, spaces, or new lines. (2) The tool removes zeros, computes the GCF, and derives the LCM. (3) Review the count of numbers processed to verify your input. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering Numbers = 24, 60, 90 returns Greatest common factor = 6, Least common multiple = 360. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Can I include negative numbers?
Yes. The calculator uses the absolute value of each integer so signs do not impact GCF or LCM results.
What happens if I enter zero?
Zero is ignored because it would make both GCF and LCM undefined. Remove zeros or replace them with a meaningful value.
What formula does the LCM & GCF Calculator use?
The calculator cleans the input list, computes the greatest common divisor across all numbers, then leverages the gcd-derived formula to produce the LCM.
How do I use the LCM & GCF Calculator?
Type integers separated by commas, spaces, or new lines. The tool removes zeros, computes the GCF, and derives the LCM. Review the count of numbers processed to verify your input.