What is the difference between GCD and LCM?

The GCD (Greatest Common Divisor) is the largest number that divides all inputs evenly. The LCM (Least Common Multiple) is the smallest number that all inputs divide into evenly. For 12 and 18, GCD is 6 and LCM is 36.

Can I compute GCD and LCM for more than two numbers?

Yes. Enter as many numbers as you need separated by commas. The tool computes the GCD and LCM of the entire set by iteratively applying the pairwise algorithm to each number in sequence.

What algorithm does the calculator use for GCD?

The calculator uses the Euclidean algorithm, which repeatedly divides the larger number by the smaller and replaces the larger with the remainder until the remainder is zero. The last non-zero remainder is the GCD. This is the most efficient method known for computing GCD.

How are GCD and LCM related?

For any two positive integers a and b, the product of GCD(a,b) and LCM(a,b) equals a × b. This means once you know the GCD, you can calculate the LCM directly as LCM = (a × b) / GCD, which is exactly how the calculator computes LCM.

What happens if one of my numbers is zero?

GCD(a, 0) = a, since every number divides zero. LCM(a, 0) = 0, since zero is the only multiple of zero. The calculator handles these cases correctly following standard mathematical conventions.

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GCD/LCM Calculator

The GCD (Greatest Common Divisor) of two numbers is the largest integer that divides both evenly, computed using the Euclidean algorithm. The LCM (Least Common Multiple) is the smallest integer both numbers divide into evenly, calculated as LCM = (a × b) / GCD. Our free calculator handles both instantly.

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What is GCD/LCM Calculator?

A GCD/LCM calculator is an online tool that computes the Greatest Common Divisor and Least Common Multiple of two or more integers using the Euclidean algorithm and the GCD-LCM product relationship, optionally displaying step-by-step working.

Complementary Tools

These tools work great alongside GCD/LCM Calculator:

Percentage Calculator Scientific Calculator

Start Using GCD/LCM Calculator Today

GCD and LCM are the building blocks of number theory and fraction arithmetic. Whether you are simplifying a fraction, finding a common denominator, or solving a scheduling problem, this free GCD/LCM calculator delivers instant results with the Euclidean algorithm steps shown — so you can verify the answer and learn the method at the same time.

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