GCD & LCM Calculator for Fast Number Calculations
Calculate the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two or more numbers instantly.
Enter your numbers to get accurate GCD and LCM results, Euclidean algorithm steps, prime factorization and mathematical relationships.
GCD & LCM Calculator
Find common divisors and multiples instantly
Enter Your Numbers
Enter at least two whole numbers.
Numbers
Add or remove numbers as needed.
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GCD & LCM Calculator
Free Online GCD and LCM Calculator
The GCD & LCM Calculator helps you calculate the Greatest Common Divisor and Least Common Multiple of two or more whole numbers quickly and accurately.
In addition to the final results, the calculator can display Euclidean algorithm steps, prime factorization and the mathematical relationship between GCD and LCM.
Features
Powerful GCD & LCM Features
Everything you need to work with common divisors and multiples.
Calculate GCD
Find the greatest common divisor of two or more integers.
Calculate LCM
Find the least common multiple of the supplied numbers.
Multiple Numbers
Enter and calculate up to 100 numbers at once.
Euclidean Algorithm
View the calculation steps used to determine the GCD.
Prime Factorization
View the prime factorization of the input numbers.
Quick Examples
Load common number combinations with one click.
Copy Results
Copy the calculation results and details to your clipboard.
Download Results
Download your calculated result as a text file.
Mobile Friendly
Use the calculator comfortably on phones, tablets and desktops.
How It Works
How to Use the GCD & LCM Calculator
Follow these simple steps to calculate GCD and LCM.
Enter Numbers
Enter at least two whole numbers.
Add More Numbers
Add additional numbers if your calculation requires them.
Calculate
Click Calculate GCD & LCM to process the numbers.
View Results
View GCD, LCM, factorization and calculation steps.
Mathematics
GCD & LCM Formulas
The calculator uses standard mathematical methods to determine the greatest common divisor and least common multiple.
Greatest Common Divisor
The GCD is the largest positive integer that divides each of the given numbers without leaving a remainder.
Least Common Multiple
For two non-zero integers, the LCM can be calculated using their product and their GCD.
Common Uses
Where GCD and LCM Are Useful
GCD and LCM are commonly used in mathematics, number theory, fractions, schedules, grouping problems and everyday calculations.
School Mathematics
Solve and verify GCD and LCM exercises.
Fractions
Find common denominators when working with fractions.
Number Theory
Explore divisibility and common factors.
Scheduling
Use LCM to identify repeating intervals.
Important Information About GCD & LCM
GCD
The GCD identifies the largest positive integer that divides all supplied numbers.
LCM
The LCM identifies the smallest positive common multiple for the supplied non-zero integers.
Euclidean Algorithm
The Euclidean algorithm repeatedly uses remainders to determine the GCD efficiently.
Prime Factorization
Prime factors can be used to understand the common factors and multiples of numbers.
FAQ
Frequently Asked Questions
What is GCD?
GCD stands for Greatest Common Divisor. It is the largest positive integer that divides each supplied number without leaving a remainder.
What is LCM?
LCM stands for Least Common Multiple. It is the smallest positive common multiple of the supplied non-zero integers.
Can I calculate GCD for more than two numbers?
Yes. This calculator supports multiple numbers and can accept up to 100 numbers.
Does the calculator show the GCD calculation steps?
Yes. The result area includes Euclidean algorithm steps when they are returned by the calculator.
Can I see prime factorization?
Yes. The result area includes a prime factorization breakdown for the input numbers.
Can I copy or download my results?
Yes. Use the Copy button to copy the result or the Download button to save the calculation as a text file.
Calculate GCD & LCM Instantly
Enter your numbers and get accurate GCD, LCM, factorization and calculation steps in seconds.
Calculate GCD & LCM