Gcd Lcm Calculator

GCD & LCM Calculator

Instantly find the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of any two numbers. This free online tool allows you to calculate GCD and LCM quickly and accurately. No sign-up or installation required.

Understanding GCD and LCM

The Greatest Common Divisor (GCD) and Least Common Multiple (LCM) are two of the most fundamental concepts in number theory, arithmetic, and algebra. They are heavily utilized when simplifying fractions, finding common denominators, and scheduling recurring events.

What is the Greatest Common Divisor (GCD)?

The GCD (also known as the Greatest Common Factor or GCF) of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder.

For example, the GCD of 12 and 18 is 6.
Divisors of 12: 1, 2, 3, 4, 6, 12
Divisors of 18: 1, 2, 3, 6, 9, 18
The largest number appearing in both lists is 6.

What is the Least Common Multiple (LCM)?

The LCM of two or more integers is the smallest positive integer that is perfectly divisible by each of the integers.

For example, the LCM of 12 and 18 is 36.
Multiples of 12: 12, 24, 36, 48...
Multiples of 18: 18, 36, 54...
The smallest matching multiple is 36.

Frequently Asked Questions

How are GCD and LCM mathematically related?↓

There is a beautiful mathematical relationship between them. For any two numbers a and b, the product of their GCD and LCM equals the product of the numbers themselves: GCD(a,b) × LCM(a,b) = |a × b|.

What algorithm does this calculator use?↓

This calculator uses the highly efficient Euclidean algorithm to determine the GCD. Once the GCD is found, it calculates the LCM using the formula: LCM = |a × b| / GCD.

Can I find the GCD and LCM of negative numbers?↓

Yes, but GCD and LCM are technically defined strictly as positive integers. Our calculator takes the absolute value of any inputs to provide the mathematically correct positive integer result.