LCM & GCF Calculator — Least Common Multiple & Greatest Common Factor

How it works

Need to find the lowest common multiple or the greatest common factor quickly? This calculator makes it easy to compare numbers, simplify fractions, and plan repeating patterns without doing long arithmetic by hand. Enter a list of integers and get the LCM, GCF (also called GCD or HCF), and clear explanations you can rely on.

What these results mean: the LCM (least common multiple) is the smallest positive number that all your inputs divide into evenly. It tells you when cycles line up, like schedules or repeating events. The GCF (greatest common factor) is the largest number that divides all inputs without a remainder. It is the key idea behind reducing fractions and comparing ratios.

Behind the scenes, the calculator uses the Euclidean Algorithm, a fast and reliable way to find the GCF by repeatedly dividing and taking remainders. Once the GCF is known, the LCM is found using the relationship \( \mathrm{LCM}(a,b)=\dfrac{|a\cdot b|}{\gcd(a,b)} \). For lists of numbers, the calculator combines them step by step until all values are included.

How to use the calculator:

1. Type or paste your integers, separated by commas, spaces, or new lines.
2. Click Calculate to see the GCF and LCM results.
3. Use Add Example Data if you want a quick sample to test the tool.
4. Clear the inputs to start a new set of numbers.

Real-world uses: LCM helps when you need a shared timeline, such as syncing class schedules, maintenance cycles, or music loops. GCF is useful for simplifying ingredient ratios, resizing images evenly, or reducing fractions in math homework. If you are working with multiple measurements or repeating intervals, these values provide quick answers and help you avoid mistakes.

Special cases handled: zeros are allowed (if any input is zero, the LCM is zero), negatives are treated by absolute value, and large integers switch to precise BigInt arithmetic so results stay accurate.

Frequently Asked Questions

Which separators can I use?

Commas, spaces, or new lines. Extra whitespace is ignored.

Can I enter negative numbers or zero?

Yes. We use absolute values for GCF/LCM. Zeros are allowed; if any number is zero, the LCM of the list is zero.

What if I enter only one number?

Then GCF = |n| and LCM = |n|.

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