The formula
How it works
The least common multiple (LCM) is the smallest number that all of your numbers divide into evenly. Enter two or three numbers to find it — the key to adding fractions with different denominators and to problems where cycles line up.
FAQ
How is the LCM linked to the GCF?
They multiply together neatly: for two numbers, the LCM times the GCF equals the product of the numbers. So once you know one, the other is easy to find.
Why do I need the LCM for fractions?
To add or subtract fractions you first give them the same denominator. The least common multiple of the denominators is the smallest common denominator, which keeps the numbers as small as possible.
What is the LCM of two prime numbers?
If both numbers are prime and different, their only shared factor is 1, so their LCM is simply their product. The same is true for any two coprime numbers, not just primes.
What is the LCM of a number with itself, or with 1?
The LCM of a number with itself is just that number, and the LCM of any number with 1 is the number itself, since every number is a multiple of 1.
How do you find the LCM of three or more numbers?
Find the LCM of the first two numbers, then find the LCM of that result with the next number, repeating until every number has been included. The order you combine them in does not change the final answer.
Can the LCM ever be smaller than the largest input number?
No — the LCM is always a multiple of every number you enter, so it can never be smaller than the largest one. It equals the largest number only when that number is itself a multiple of all the others.
Where do LCMs show up outside of fractions?
Anywhere repeating cycles need to sync up, such as traffic lights on different timers, work shifts that rotate on different schedules, or planets aligning in astronomy — the LCM tells you how long until they all line up again.
About the least common multiple calculator
This calculator finds the least common multiple of two or three whole numbers — the smallest number that each of them divides into without a remainder. The LCM is a companion to the greatest common factor, and together they are the two most useful facts about how numbers share factors. It is the tool you reach for when fractions need a common denominator, or when repeating events need to line up.
How to use it
Enter two numbers, or add a third, leaving the last box at zero if you only need two. The calculator returns their least common multiple. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into. That makes 12 the least common denominator when adding quarters and sixths. If two numbers share no factors, their LCM is simply their product.
The formula
For two numbers the LCM is found from the GCF using : multiply the numbers, then divide by their greatest common divisor to remove the overlap counted twice. For three numbers, take the LCM of the first two and then the LCM of that with the third. Because dividing by the GCF keeps the result as small as possible, this always gives the least common multiple, not just any common one.
Where it is used
The most common use is adding and subtracting fractions, where the least common denominator is the LCM of the denominators. It also solves timing puzzles: if one bus comes every 4 minutes and another every 6, they arrive together every 12 minutes — their LCM. Gears, schedules, and repeating patterns all rely on the same idea, and in music the LCM explains when overlapping rhythms come back into step.