🧮 GCD and LCM Calculator
Calculate the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two or more numbers.
GCD and LCM Calculator
The GCD and LCM Calculator computes the Greatest Common Divisor and Least Common Multiple of any set of positive integers. These two fundamental number theory concepts are essential for fraction simplification, least common denominator finding, and many algorithmic applications.
Enter two or more comma-separated numbers to compute their GCD and LCM. The GCD is useful for reducing fractions to their simplest form, while the LCM is used to find common denominators for addition and subtraction of fractions. Both are widely used in number theory, cryptography, and computer science.
This calculator uses the efficient Euclidean algorithm for GCD computation and derives the LCM from the GCD. It handles any number of inputs and provides instant, accurate results for numbers of any reasonable size.
Frequently Asked Questions
What is the GCD?
The Greatest Common Divisor (GCD) is the largest positive integer that divides all given numbers without a remainder. For example, GCD(12, 18) = 6, since 6 is the largest number that divides both 12 and 18.
What is the LCM?
The Least Common Multiple (LCM) is the smallest positive integer that is a multiple of all given numbers. For example, LCM(4, 6) = 12, since 12 is the smallest number divisible by both 4 and 6.
What is the relationship between GCD and LCM?
For two numbers a and b: GCD(a,b) × LCM(a,b) = a × b. This means if you know the GCD, you can find the LCM (and vice versa) using the product of the two numbers.