GCF and LCM calculator, with the steps.

A GCF calculator finds the greatest common factor of a set of numbers: the biggest whole number that divides all of them exactly. An LCM calculator finds the least common multiple: the smallest number that all of them divide into exactly. This page works out both for up to ten numbers at once and shows the working four ways, so you can match the method your class or textbook uses. Big numbers are fine, because the page uses exact whole-number arithmetic with no rounding.

How to use the GCF and LCM calculator

1. Type your whole numbers in Numbers (2 to 10), separated by spaces, commas or new lines.
2. Read the two big cards: Greatest common factor (GCF) and Least common multiple (LCM).
3. Choose how to see the working under Show the working: Prime factors, Euclidean algorithm, Listing or Ladder (cake).
4. With two numbers, the card under the answers also shows the fraction in lowest terms.
5. Use Copy result to copy the answers, or Copy link to share your numbers.

Method 1: prime factorisation

Split each number into primes. 12 = 2² × 3 and 18 = 2 × 3². For the GCF, keep the primes both numbers share, each to its lowest power: 2 and 3, so 2 × 3 = 6. For the LCM, keep every prime that appears, each to its highest power: 2² and 3², so 4 × 9 = 36. The page lays the primes out in a table with the lowest and the highest power of each, so you can see where the answers come from.

Method 2: the Euclidean algorithm

This method needs no factoring, so it works for huge numbers. Divide the bigger number by the smaller and keep the remainder. Repeat with the smaller number and the remainder until the remainder is 0. The last non-zero remainder is the GCF. For 48 and 18: 48 = 2 × 18 + 12, then 18 = 1 × 12 + 6, then 12 = 2 × 6 + 0. The GCF is 6. For two numbers, LCM = a × b ÷ GCF, so the LCM of 48 and 18 is 48 × 18 ÷ 6 = 144. For more numbers the page works through them one at a time.

Method 3: listing

List all the factors of each number and pick the biggest one in every list. The factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 18 are 1, 2, 3, 6, 9 and 18. The shared ones are 1, 2, 3 and 6, so the GCF is 6. For the LCM, list multiples instead. Multiples of 4 are 4, 8, 12 and multiples of 6 are 6, 12, so the LCM of 4 and 6 is 12. Listing is easy to follow but gets long, so the page only does it for numbers up to 1,000,000.

Method 4: the ladder or cake method

Write the numbers in a row. Find a prime that divides at least two of them, write it on the left, and divide. Numbers the prime does not divide are brought down. Keep going until no prime divides two numbers in the bottom row. For 12, 18 and 30: divide by 2 to get 6, 9, 15, then by 3 to get 2, 3, 5. No prime divides two of those. The GCF is the product of the primes that divided every number: 2 × 3 = 6. The LCM is all the primes on the left times the bottom row: 2 × 3 × 2 × 3 × 5 = 180.

What the GCF and LCM are used for

Special cases

• If the GCF is 1, the numbers are coprime (also called relatively prime). Then the LCM of two numbers is just their product.
• The GCF of a number and 0 is that number, so GCF(0, 5) = 5. The LCM of any list containing 0 is 0. A list of only zeros has no GCF.
• Negative numbers use their absolute value, and the page says so.
• Very large numbers cannot always be split into primes in the time the page allows. The Euclidean algorithm still works, and the page says when a method cannot finish.

For the factors and prime factorisation of one number, use the factor calculator. To simplify and add fractions with the working shown, use the fraction calculator, and for the remainder of a division, the remainder calculator.