Find the least common multiple of any numbers. This free LCM calculator returns the smallest value they all divide into, and shows the greatest common factor too.
Enter two or more whole numbers. The LCM is the smallest positive number that every value divides into evenly.
The LCM is useful for adding fractions (a common denominator) and for problems where events repeat on different cycles. It uses whole numbers; decimals are rounded.
How the LCM Calculator Works
The least common multiple (LCM) is the smallest positive number that every number in your list divides into evenly. This calculator accepts two or more whole numbers and returns their LCM, along with the greatest common factor (GCF) of the same set.
Formula: For two numbers, LCM(a, b) = |a × b| ÷ GCF(a, b), where GCF is found with the Euclidean algorithm (repeatedly replacing the larger number with the remainder of dividing it by the smaller, until the remainder reaches 0). For a list of three or more numbers, the calculator applies this pairwise formula in sequence — combining the first two numbers, then combining that result with the next number, and so on until every value has been included. Decimal inputs are rounded to whole numbers first, and zeros are excluded.
- Numbers — the list of two or more whole numbers you want the LCM (and GCF) of, separated by commas, spaces, or new lines
Example Scenarios
| Numbers | LCM | GCF |
|---|---|---|
| 4, 6 | 12 | 2 |
| 6, 8 | 24 | 2 |
| 4, 6, 8 | 24 | 2 |
| 5, 10, 15 | 30 | 5 |
| 9, 12 | 36 | 3 |
| 7, 3 | 21 | 1 |
LCM Calculator FAQ
What’s the difference between LCM and GCF?
The LCM (least common multiple) is the smallest number every value in your list divides into evenly, so it’s always equal to or larger than your biggest number. The GCF (greatest common factor) is the largest number that divides evenly into every value, so it’s always equal to or smaller than your smallest number.Why is the LCM useful for adding fractions?
To add or subtract fractions with different denominators, you first need a common denominator. Using the LCM of the denominators as that common denominator keeps the numbers as small as possible, which makes the arithmetic easier than using any other shared multiple.Can I find the LCM of more than two numbers?
Yes. Enter as many whole numbers as you like, separated by commas, spaces, or new lines. The calculator finds the LCM of the first two, then combines that result with each additional number in turn until all of them are accounted for.What happens if I enter a decimal number?
The calculator rounds any decimal input to the nearest whole number before calculating, since the least common multiple is only defined for whole numbers. Enter whole numbers directly if you want to avoid any rounding.Does entering 0 affect the LCM calculation?
Zero values are filtered out automatically, and the LCM is calculated from the remaining nonzero numbers only, since a multiple of zero doesn’t produce a meaningful smallest common value.How is the LCM different from the product of the numbers?
The product is simply all the numbers multiplied together, shown separately as a reference figure. The LCM is usually smaller than the product because it accounts for shared factors between the numbers — the product and LCM only match when the numbers share no common factors.Related Calculators
Need just the greatest common factor on its own? The GCF calculator handles that half of the pair. If your LCM is meant for combining fractions, the fraction simplifier can reduce the result afterward, and the fraction calculator can carry out the full addition once you have a common denominator.