Calculate GCD and LCM from multiple values

Calculator for finding the greatest common divisor and the least common multiple of two or more natural numbers. Please enter multiple natural numbers separated by spaces. The GCD and LCM of these numbers will be calculated.

Example: The greatest common divisor of the three natural numbers 78 102 144 is 6. All three of these numbers are divisible by 6 without a remainder and by no larger number. The least common multiple is 31824. This is the product of all three numbers divided by 36.

The GCD of two values ​​is calculated using the Euclidean algorithm, which was first described by the Greek mathematician Euclid almost 2,500 years ago. The LCM of two values ​​is one value multiplied by the other value divided by their GCD. The GCD and LCM of multiple values ​​are calculated by first determining the GCD and LCM of the first two values, then the GCD and LCM of the result with the third value, and so on. This works because both GCD and LCM are associative, meaning the order in which they are combined doesn't matter.
The least common multiple is also known as the lowest common multiple. The greatest common divisor of different numbers is always smaller than the least common multiple of these numbers.

A divisor of a natural number is another natural number by which the first is divisible without a remainder. Instead of divisor, you could just as well say denominator or factor, so another term for GCD is GCF. A multiple of a natural number is that number multiplied by another natural number. The greatest divisor and the least multiple are special features of individual numbers. The least divisor of natural numbers, on the other hand, is always 1, and the greatest multiple is always infinity.