What is the difference between GCD and LCM?

The Greatest Common Divisor (GCD) is the largest number that divides two or more numbers evenly, while the Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, for 12 and 18: GCD = 6 (largest number dividing both), LCM = 36 (smallest multiple of both).

How is GCD used in simplifying fractions?

GCD is essential for reducing fractions to their simplest form. To simplify a fraction, divide both the numerator and denominator by their GCD. For example, to simplify 24/36, find GCD(24, 36) = 12, then divide: 24÷12 / 36÷12 = 2/3.

Why is LCM important for adding fractions?

When adding fractions with different denominators, you need a common denominator. The LCM of the denominators gives you the least common denominator (LCD), making calculations simpler. For example, to add 1/6 + 1/8, find LCM(6, 8) = 24, which becomes your common denominator.

What's the relationship between GCD and LCM?

For any two numbers a and b, there's a mathematical relationship: a × b = GCD(a, b) × LCM(a, b). This means if you know three of these values, you can calculate the fourth. This relationship is useful for verification and alternative calculation methods.

Can GCD and LCM be calculated for more than two numbers?

Yes! Both GCD and LCM can be calculated for any quantity of numbers. For GCD, find the common divisor of all numbers. For LCM, find the smallest number that all input numbers divide into evenly. Our calculator supports multiple numbers for both operations.

Math

GCD & LCM

Calculate greatest common divisor and least common multiple.

How to Use This Calculator

Enter your numbers

Input two or more integers for which you want to find the GCD and LCM. The numbers can be any positive integers, and there's no practical limit to how many you can enter.

Choose calculation type

Select whether you want to calculate GCD, LCM, or both simultaneously. Many users choose to calculate both since they're often used together in problem-solving.

Understand the results

Review the calculated GCD and LCM values. The calculator may also show the prime factorization method or Euclidean algorithm steps, helping you understand how these values were derived.