Free GCF and LCM Calculator
Greatest common factor and least common multiple of two integers.
- Free Forever
- No Registration Required
- Instant Results
- Downloadable Reports
- Mobile Friendly
Inputs
Result
GCF (greatest common factor)
12
Your result is ready.
Download your free detailed report — inputs, result, formula and explanation included.
Estimates only. Verify with a professional for consequential decisions.
- Always Free
- No Hidden Costs
- No Account Required
- Unlimited Calculations
- Instant Reports
Short answer
GCF = Euclidean(a, b). LCM = |a·b| ÷ GCF(a, b). The two are linked — knowing one gives the other in one step.
What is the GCF and LCM Calculator?
GCF is the largest integer dividing both numbers; LCM is the smallest positive integer both divide into.
How does the GCF and LCM Calculator work?
Compute GCF via the Euclidean algorithm. LCM equals the product divided by GCF.
Formula
Variables
Euclideangcd(a, b) = gcd(b, a mod b)
Explanation
Euclid's algorithm reaches the GCF in O(log min(a, b)) steps.
Examples
Example 1: 24 and 36
GCF = 12, LCM = 72.
Applications
- Fraction simplification
- Scheduling repeating events
- Number theory homework
Advantages
- Runs instantly on numbers of any reasonable size
Limitations
- Two operands — chain manually for more
Common mistakes
- Listing all factors instead of using the Euclidean algorithm (works but slow)
Tips
- For three numbers: GCF(a, b, c) = GCF(GCF(a, b), c). Same for LCM.
Related concepts
The GCF and LCM Calculator sits inside the Math Calculators hub, in the number tools & notation cluster. Bases, factors, rounding and precision. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.
Practical use cases and industry applications
Understanding GCF and LCM
GCF is the largest integer dividing both numbers; LCM is the smallest positive integer both divide into. Within math calculators, gcf and lcm belongs to the number tools & notation cluster, where it shares terminology and assumptions with closely related tools.
Learning how gcf and lcm is calculated
Euclid's algorithm reaches the GCF in O(log min(a, b)) steps. Working through the variables one at a time — Euclidean — makes the result reproducible by hand and easier to sanity-check.
Using gcf and lcm to make a decision
Fraction simplification Scheduling repeating events Number theory homework Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.
How gcf and lcm compares with related measures
base, factor, notation, precision all describe adjacent aspects of number tools & notation. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.
Frequently asked questions
Are GCF and GCD the same?
Yes. Greatest Common Factor and Greatest Common Divisor are two names for the same thing.
Related calculators
These tools share entities, formulas or user intent with the gcf and lcm calculator.
Math
Free Prime Number Calculator
Check primality and list all prime factors.
Math
Free Fraction Calculator
Add, subtract, multiply, or divide two fractions with simplification.
Math
Free Divisors & LCM Chain Calculator
All divisors, GCD and LCM across up to four numbers.
Math
Free Half-Life Calculator
Amount remaining after time for exponential decay.
Math
Free Matrix Calculator (2×2)
Determinant and inverse of a 2×2 matrix.
Math
Free Rounding Calculator
Round to decimal places, integer, tens, hundreds, thousands.
Math
Free Scientific Notation Calculator
Convert a number to and from scientific notation.
Math
Free Significant Figures Calculator
Round a number to a chosen number of sig figs.
Math
Free 3D Cross Product Calculator
Cross product and magnitude of two 3D vectors.