LCM calculator

Type two or more whole numbers, separated by commas or spaces, such as 12, 18 or 4 6 10. The least common multiple appears straight away, with the prime factors and, for two numbers, a Venn diagram below. The greatest common factor is shown beside it. Up to 10 numbers work, each up to a trillion, and the answer stays exact however large it gets.

The multiples of a number are its times table, so 12, 24, 36, 48 and on for 12, and 18, 36, 54 for 18. The smallest number in both lists, 36, is the least common multiple. It's sometimes called the lowest common multiple, and when the numbers are the bottoms of fractions, the lowest common denominator.

That's its everyday use. To add 5/12 and 7/18, rewrite both over 36, as 15/36 and 14/36, and the sum is 29/36. It also answers when-do-they-meet puzzles. If one bus comes every 12 minutes and another every 18, and both leave together, they next leave together 36 minutes later.

Write each number as a product of primes, so 12 = 2² × 3 and 18 = 2 × 3². Then take every prime that appears in any of them, each to the highest power it reaches, here 2² and 3². The LCM is 2² × 3² = 36. In the Venn diagram, that's everything in both circles multiplied together, with the overlap counted once.

For two numbers there's a shortcut that makes a good check. Multiply them and divide by their greatest common factor, as in 12 × 18 ÷ 6 = 36. For three or more, work it out two at a time. The LCM of 4, 6 and 10 is the LCM of 12 (from 4 and 6) and 10, which is 60.