GCD & LCM of a List Calculator

This calculator finds the greatest common divisor and the lowest common multiple of a whole list of numbers at once, not just two. The greatest common divisor, or GCD, also called the highest common factor, is the largest whole number that divides evenly into all the numbers in your list. The lowest common multiple, or LCM, is the smallest number that all of them divide into evenly. These two are everywhere in mathematics: the GCD simplifies fractions to their lowest terms and finds the biggest equal grouping, while the LCM finds common denominators for adding fractions and works out when repeating events coincide, such as cycles or schedules lining up. Doing this for several numbers by hand means finding all the factors or prime factorisations, which is tedious and error-prone. This tool does it instantly for any number of values. You paste or type your list of whole numbers, and the calculator returns the GCD and the LCM of the entire list, along with the count of numbers and the list itself. The results update as you type. Use it to simplify fractions, to find a common denominator, to solve when cycles align, or for number theory homework. The calculator works through the list two at a time, using the efficient Euclidean algorithm for the GCD, which repeatedly replaces the larger number with the remainder of dividing the two until one becomes zero, and then derives the LCM from the relationship that the product of two numbers equals their GCD times their LCM. Applying this pairwise across the list gives the GCD and LCM of them all. The numbers should be positive whole numbers; the GCD of the list is at least one, and the LCM grows quickly as you add numbers with few common factors.

GCD is the largest number dividing all; LCM is the smallest number all divide into. Uses the Euclidean algorithm pairwise. Enter positive whole numbers.