LCM Calculator
Least Common Multiple Tool
Understanding the Least Common Multiple
The Least Common Multiple ties together the multiplication tables of every number in a set — it's the smallest number they all divide into evenly, and it's the key to adding fractions with unlike denominators.
Breaking each number into its prime building blocks makes the LCM straightforward: take the highest power of every prime that appears anywhere in the set, and multiply them together.
If one bus arrives every 12 minutes and another every 18 minutes, the LCM (36) tells you exactly when they'll next arrive together — a classic scheduling application.
Worked Example
To find the LCM of 12 and 18: 12 = 2² × 3 and 18 = 2 × 3². Taking the highest power of each prime gives 2² × 3² = 4 × 9 = 36, so the LCM of 12 and 18 is 36.
Key Takeaways
- The LCM is always a multiple of every input number, and it's the smallest one that satisfies all of them at once.
- The prime factorization method scales to any number of inputs, not just two — add as many rows as your problem needs.
- LCM and GCF are closely related. For two numbers, their LCM multiplied by their GCF always equals the product of the two numbers.
Frequently Asked Questions
- Type a positive whole number into each row.
- Click "Add Number" to include more than two numbers, or the icon to remove a row.
- Click "Calculate" to see the least common multiple, along with the prime factorization of every number involved.
The Least Common Multiple (LCM) of a set of numbers is the smallest positive number that every number in the set divides into evenly. For example, the LCM of 4 and 6 is 12, since 12 is the smallest number that both 4 and 6 divide into with no remainder.
Every whole number greater than 1 can be broken down into a unique product of prime numbers. To find the LCM, break each number down into its prime factors, then for every prime that appears in any of the numbers, take the highest power of that prime seen across all of them, and multiply those highest powers together. This guarantees the result is the smallest number divisible by every input.
Yes. Add as many rows as you need — the same prime factorization method extends naturally to any number of inputs, since you just take the highest power of each prime across the whole set instead of just two numbers.
The LCM is most commonly used to find a common denominator when adding or subtracting fractions with different denominators. It also shows up in scheduling problems, like figuring out when two repeating events (such as buses arriving every 12 and 18 minutes) will next happen at the same time.
The Least Common Multiple is only defined for positive whole numbers, so the calculator shows a clear error if any entry is zero, negative, or not a whole number.