Find the greatest common factor and least common multiple for any list of numbers.
| Number | Prime Factorisation |
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Enter two or more positive whole numbers separated by commas, then calculate. The calculator finds the greatest common factor (the largest number that divides evenly into all of them) and the least common multiple (the smallest number that all of them divide evenly into), along with the prime factorisation of each number.
The greatest common factor (GCF), also called the greatest common divisor (GCD), is the largest positive integer that divides evenly into every number in the list. For example, the GCF of 12 and 18 is 6, since 6 is the largest number that divides into both without a remainder.
The least common multiple (LCM) is the smallest positive integer that every number in the list divides into evenly. For example, the LCM of 4 and 6 is 12, since 12 is the smallest number that both 4 and 6 divide into without a remainder. LCM is commonly used when finding a common denominator to add or subtract fractions.
The GCF of a list of numbers can be found by computing the GCF of the first two numbers, then computing the GCF of that result with the next number, and repeating through the whole list. The Euclidean algorithm makes each pairwise step efficient even for large numbers.
For any two numbers, the product of their GCF and LCM equals the product of the two numbers themselves: GCF(a,b) × LCM(a,b) = a × b. This relationship is a useful shortcut for finding one value if you already know the other.
To add or subtract fractions with different denominators, the denominators first need to be converted to a common one. Using the least common multiple of the denominators as that common denominator keeps the numbers as small as possible, which makes the arithmetic simpler than using any other common multiple.