GCF / LCM Calculator
Calculate Greatest Common Factor and Least Common Multiple
About the GCF / LCM Calculator
The greatest common factor and least common multiple are workhorses of arithmetic — you need the GCF to simplify fractions and the LCM to add them. This calculator finds both for two or more numbers at once, and shows the prime factorizations and the Euclidean-algorithm steps behind the answers.
Students use it throughout fraction work and number theory; it also turns up in scheduling problems, where the LCM tells you when repeating events coincide. Beyond the answers, it verifies them — confirming that GCF times LCM equals the product of the numbers — and lays out Euclid's method step by step.
How to Use the GCF / LCM Calculator
- Enter two or more whole numbers, separated by commas.
- Read the GCF (greatest common factor) and the LCM (least common multiple).
- Review the prime factorization of each number.
- Follow Euclid's algorithm steps and the verification that GCF × LCM equals the product.
Why Use ToolForge’s GCF / LCM Calculator
- It computes both the GCF and the LCM together for any list of numbers, not just a pair.
- It shows each number's prime factorization and the full Euclidean-algorithm steps, making the method visible.
- It verifies the result by checking that GCF × LCM equals the product of the inputs, so you can trust the answer.
- It runs locally and instantly, with no sign-up.
Frequently Asked Questions
What is the difference between GCF and LCM?
The greatest common factor is the largest number that divides all your values evenly — used to simplify fractions. The least common multiple is the smallest number all your values divide into — used to find a common denominator. This calculator gives both.
How does Euclid's algorithm find the GCF?
It repeatedly replaces the larger number with the remainder of dividing it by the smaller, until the remainder is zero; the last non-zero value is the GCF. The calculator shows each division step so you can follow the process.
How are GCF and LCM related?
For any two numbers, their GCF multiplied by their LCM equals the product of the numbers themselves. The calculator uses this relationship as a verification check, marking the result correct when it holds.
Where is the LCM used in real life?
The least common multiple answers "when do repeating cycles line up again?" — when two buses on different schedules next depart together, or when adding fractions with unlike denominators. The GCF, by contrast, shows up whenever you reduce a fraction to simplest form.
