LCM Calculator (Least Common Multiple)

The least common multiple (LCM) of a set of integers is the smallest positive whole number that every one of them divides into with no remainder. For 4 and 6 it is 12, because 12 is the first number that both 4 and 6 fit into evenly.

For two numbers the LCM equals their product divided by their greatest common divisor: lcm(a, b) = |a x b| / gcd(a, b). For a longer list the calculator applies this rule to the first two values, then to that result and the next value, and so on until the whole list is folded into a single answer.

Use commas, spaces, or both. Inputs like '4, 6', '4 6', and '4,6' all parse the same way, and empty gaps between separators are ignored, so a stray extra comma will not break the result.

Yes. With a single value the LCM is simply that number itself, since it is trivially the smallest multiple of one number. The tool needs at least one integer and will prompt you if the box is empty.

Zero is rejected because the multiple of zero is always zero, which leaves the LCM undefined. Decimals and negatives are rejected too, because the least common multiple is only defined for positive integers.

When two numbers share no common factor, their greatest common divisor is 1, so the LCM is simply their product. For example lcm(2, 7) is 14 and lcm(9, 25) is 225.

For any two positive integers the product of their LCM and GCD equals the product of the numbers themselves: lcm(a, b) x gcd(a, b) = a x b. That relationship is exactly why dividing by the GCD gives the LCM.

The LCM of the denominators is the least common denominator. Rewriting fractions over that shared denominator lets you add, subtract, or compare them without changing their values, so 1/4 and 1/6 both become sixths of twelve.

The math is exact while values stay within JavaScript's safe integer range of about 9 quadrillion; beyond that the LCM can grow large enough to lose precision. Everything runs in your browser, so nothing you type is uploaded or stored.