LCM Calculator

Find the least common multiple of two or more numbers, with every pairwise step shown so you can see exactly how the answer was reached.

Least common multiple —

How to Find the LCM

Enter any list of whole numbers to see the least common multiple and the working.

1

Enter your numbers

Type two or more positive whole numbers separated by commas or spaces, like 4, 6. Decimals are truncated and duplicates are fine.

2

The calculator reduces pairwise

It computes lcm(a, b) = a × b / gcd(a, b) on the first two numbers, then combines that result with the next number, and so on, until every number has been folded in.

3

Read the result and steps

The least common multiple appears at the top, and each pairwise reduction is listed below it. Need the largest shared factor instead? The GCF Calculator works the same list of numbers the other way.

Frequently Asked Questions

What is the LCM (least common multiple)?
The least common multiple (LCM) of two or more numbers is the smallest positive whole number that every one of them divides into evenly. The LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into with no remainder — no smaller shared multiple exists. This calculator finds it with lcm(a, b) = a × b / gcd(a, b), reusing the greatest common factor so it stays fast even for large numbers.
What is the difference between LCM and GCF?
The LCM (least common multiple) is the smallest number that every number in a set divides into evenly, while the GCF (greatest common factor) is the largest number that divides evenly into every one of them. LCM grows up toward their shared multiples and is used to find a common denominator when adding fractions; GCF shrinks down toward their shared factors and is used to simplify fractions. For 4 and 6, the LCM is 12 and the GCF is 2. Use the GCF Calculator when you need the factor instead of the multiple.
How do you find the LCM using prime factorization?
Break each number down into its prime factors, then multiply together every prime that appears in any of them, each raised to the highest power it appears with. For 12 and 18: 12 = 2² × 3 and 18 = 2 × 3², so taking the highest power of each prime gives 2² and 3², for an LCM of 4 × 9 = 36. This calculator instead uses the a × b / gcd(a, b) formula, which reaches the same answer without factoring large numbers by hand first — prime factorization gets slow once the numbers get big.
How do you find the LCM of three or more numbers?
Reduce the list pairwise: find the LCM of the first two numbers, then find the LCM of that result and the third number, and keep going until every number has been folded in. Because the LCM is associative, the order you combine them in does not change the final answer. Enter all your numbers separated by commas or spaces and this calculator shows each pairwise reduction it performs to reach the result.