Least Common Multiple Calculator: Three Ways to Find the LCM

Least common multiple sounds like a school-only idea until you are adding fractions with different denominators, or working out when two repeating schedules land on the same minute again. Then it is just arithmetic.

What the LCM actually tells you

List the multiples of 6: 6, 12, 18, 24, 30, 36. Now list the multiples of 8: 8, 16, 24, 32, 40. The first number appearing in both lists is 24. So is 48, and so is 72, but 24 is the smallest, which is what "least" is doing in the name.

People often assume the answer is just the two numbers multiplied together. Sometimes it is. For 6 and 8 that would give 48, which is double the real answer. The product only works when the two numbers share no factors.

Three ways to find it

Listing the multiples, as above, is the first way, and it is quick enough for numbers under about 20. Beyond that the lists get long before they meet, so use one of the next two.

The GCD shortcut

For two numbers, LCM(a, b) = a x b divided by GCD(a, b). Try 18 and 24. The product is 432. The greatest common divisor is 6. So the LCM is 432 divided by 6, which is 72. Check it: 72 divided by 18 is 4, and 72 divided by 24 is 3. Both whole. Use this one in your head, because spotting a GCD is easy and spotting an LCM is not.

Prime factorisation

This one handles three or more numbers at once. Break each number into primes, then take the highest power of each prime that appears anywhere. For 12, 18 and 30: 12 is 2 squared times 3, 18 is 2 times 3 squared, 30 is 2 x 3 x 5. The highest powers are 2 squared, 3 squared and 5, so the LCM is 4 x 9 x 5 = 180. It divides all three: 180 over 12 is 15, over 18 is 10, over 30 is 6.

The GCD shortcut does not extend directly to three numbers, but you can chain it. Find the LCM of the first pair, then find the LCM of that result and the third number. Same answer, more steps.

Where it turns up outside a maths lesson

Adding fractions is the common one. To add 3/4 and 5/6 you need a common denominator, and the LCM of 4 and 6 is 12. So 3/4 becomes 9/12, 5/6 becomes 10/12, and the sum is 19/12, or 1 and 7/12. Using 24 instead would work but leaves you simplifying afterwards for no reason.

Timetables are the other one. A bus leaves every 12 minutes and a tram every 18, both at 07:00. They next depart together after 36 minutes, at 07:36, because 36 is the LCM. Packaging works the same way: hot dogs in tens and buns in eights first match at 40, which is four packs of one and five of the other.

How to use the least common multiple calculator

Type your numbers into the input box, separated by commas or spaces, and press calculate. Most versions accept more than two at once, which is where the tool saves real time. Use positive whole numbers only. Zero has no useful LCM, and negatives are treated by their absolute value.

The output gives the LCM and usually the prime factorisation it used, which is worth reading if you are checking homework. If you are working with fractions, the LCM of the denominators is your lowest common denominator, and the fraction calculator will do that step for you as part of the sum.

Common questions

What is the difference between LCM and GCF? The greatest common factor is the largest number that divides into both. The least common multiple is the smallest number both divide into. For 18 and 24 the GCF is 6 and the LCM is 72. GCF is always less than or equal to the smaller number, LCM is always greater than or equal to the larger one.

Can the LCM be one of the numbers I entered? Yes, when one number divides the other cleanly. The LCM of 4 and 12 is 12, because 12 is already a multiple of 4. No calculation needed.

What if the numbers have nothing in common? Then the LCM is simply the product. 7 and 9 share no factors, so their LCM is 63. Two different prime numbers always behave this way.

Is there a limit on how many numbers I can enter? Practically, no, though the answer grows quickly. The LCM of every number from 1 to 10 is 2,520, and by 1 to 20 it is 232,792,560.