LCM calculator (least common multiple)

What the LCM is

The least common multiple of two or more whole numbers is the smallest number that all of them divide into exactly. For 4 and 6 it is 12: the multiples of 4 are 4, 8, 12, 16 … and of 6 are 6, 12, 18 …, and 12 is the first one they share. You need it to add fractions with different denominators, and for questions such as "two buses leave every 12 and 18 minutes; when do they next leave together?" (after 36 minutes).

Method 1: from the GCF

For two numbers, LCM = first × second ÷ GCF. For 48 and 36 the GCF is 12, so the LCM is 48 × 36 ÷ 12 = 144. For more numbers, find the LCM of the first two, then the LCM of that and the next number, and so on.

Method 2: prime factors

Write each number as a product of primes and take every prime that appears, each to the highest power that appears in any of the numbers. 48 = 2⁴ × 3 and 36 = 2² × 3², so the LCM is 2⁴ × 3² = 16 × 9 = 144. The page shows this form so the two methods can be compared.

LCM and HCF

For two numbers, LCM × GCF = the two numbers multiplied together: 144 × 12 = 48 × 36 = 1,728. That is a quick check. (This product rule does not hold for three or more numbers.)

Size

The LCM can be much bigger than the numbers you type, so the page uses exact whole-number arithmetic with no upper limit on the answer.