LCM Calculator

1. Type or paste two or more whole numbers, separated by commas, spaces or new lines.
2. The least common multiple appears instantly, along with the greatest common divisor.
3. Use the LCM to add fractions, sync repeating events or solve number-theory problems.

Here is what each result means:

The least common multiple of a set of whole numbers is the smallest positive number that each of them divides into without a remainder. Every set of numbers has infinitely many common multiples, and the LCM is simply the first one you reach when counting upward.

It is the natural partner of the greatest common divisor. Where the GCD is the largest factor numbers share, the LCM is the smallest multiple they share, and the two are linked by a neat rule for any pair: a * b = gcd(a,b) * lcm(a,b).

It finds the LCM two numbers at a time, using the greatest common divisor to keep the result exact and avoid overflow.

For a pair, the LCM is lcm(a,b) = (a * b) / gcd(a,b). For more numbers it folds the list together, taking the LCM of the running result with each new value, so lcm(a,b,c) = lcm(lcm(a,b),c).

1. Find the greatest common divisor of the first two numbers.
2. Multiply them and divide by that divisor to get their LCM.
3. Repeat, combining the running LCM with each remaining number.

Dividing by the GCD first keeps the numbers small, which matters for large inputs.

Find the LCM of 4 and 6. Their greatest common divisor is 2, so lcm(4,6) = (4 * 6) / 2 = 12. Twelve is the first number both 4 and 6 divide into evenly.

Add a third number, 8. The LCM of 12 and 8 has GCD 4, giving (12 * 8) / 4 = 24, so the LCM of 4, 6 and 8 is 24. Listing multiples confirms it: 24 is the smallest value that appears in the times tables of all three.

For coprime numbers such as 3, 5 and 7, which share no factors, the LCM is simply their product, 105.

The two ideas are opposites that work together, and telling them apart avoids a lot of confusion.

Notice that 12 times 18 is 216, which equals 6 times 36, the GCD times the LCM. To explore the plain factors behind these, the percentage calculator is not the tool, but a factor list is a good next step.

The LCM depends entirely on the numbers and their shared factors, and a few patterns are worth knowing.

Shared Factors

The more factors numbers have in common, the smaller their LCM relative to their product, because less multiplication is needed to line them up.

Coprime Numbers

When numbers share no common factor, their LCM is simply the product of them all, the largest it can be.

One Number Dividing Another

If the largest number is a multiple of the rest, it is itself the LCM, as with 3, 6 and 12.

Adding a Number

Each new value can only keep the LCM the same or push it higher, never lower.

Adding and Subtracting Fractions

The LCM of the denominators is the least common denominator, the smallest base that lets you combine fractions cleanly.

Syncing Repeating Events

Two events that repeat every few days next coincide after the LCM of their cycles, useful for schedules and gears.

Number-theory and Coding Problems

Many puzzles and algorithms rely on the LCM to find the first shared point of two or more cycles.

1. Confusing LCM with GCD

The LCM is the smallest shared multiple; the GCD is the largest shared factor. They are opposites.

2. Just Multiplying All the Numbers

That gives a common multiple, but not the least one unless the numbers are coprime.

3. Forgetting to Divide by the GCD

For a pair, multiply then divide by the GCD; skipping that step overshoots the true LCM.

4. Using Non-whole Numbers

The LCM is defined for positive whole numbers. Decimals and negatives are ignored here.

5. Stopping at the First Common Multiple You Spot

List carefully; the least common multiple is easy to overshoot by eye.

The result is exact for the whole numbers you enter, using integer arithmetic that avoids rounding.

It is the smallest positive number that every number in your set divides into evenly. For 4 and 6 the LCM is 12, the first multiple both share.

Multiply them and divide by their greatest common divisor: lcm(a, b) = a x b / gcd(a, b). For 4 and 6 that is 24 / 2 = 12.

It is 12. The multiples of 4 are 4, 8, 12 and of 6 are 6, 12, so 12 is the smallest they share.

The LCM is the smallest multiple numbers share, while the GCD is the largest factor they share. For any pair, a x b equals gcd times lcm.

Take the LCM of the first two, then the LCM of that result with the next number, and so on. This calculator folds the whole list for you.

Most often to find a least common denominator when adding fractions, and to work out when two repeating cycles or events next line up.

If numbers share no common factor, their LCM is simply the product of them all. For 3, 5 and 7 the LCM is 105.

No. The LCM is always at least as large as the biggest number in the set, and equals it when that number is a multiple of the others.

No. The calculation runs in your browser, and nothing you enter is sent anywhere unless you Save a result, which stays on this device only.

• Least common multiple (Maths Is Fun).
• Least common multiple (Wikipedia).
• Greatest common factor (Maths Is Fun).