How to Find the LCM: Three Methods and One Shortcut
Listing multiples works until the numbers get awkward. The GCD shortcut handles 21 and 55 in a single line.
Quick answer: The least common multiple of two numbers is the smallest number both divide into exactly. For 12 and 18 it is 36. The fastest general method is to multiply the two numbers and divide by their greatest common divisor: 12 x 18 = 216, and 216 divided by their GCD of 6 gives 36.
Almost everyone meets the LCM while adding fractions and then never hears the name again, even though they keep using the idea. The concept is small. The methods differ mainly in how well they hold up once the numbers stop being friendly.
Three methods, one that scales
Listing multiples is the method taught first. Write out 12, 24, 36, 48 and then 18, 36, 54, and the first number appearing in both lists is 36. That is fine for small numbers. Try it with 21 and 55 and you will be writing until you reach 1,155.
Prime factorisation
Break each number into primes and take the highest count of each prime that appears in either. 12 is 2 x 2 x 3. 18 is 2 x 3 x 3. The most 2s in either number is two of them, and the most 3s is two of them, so the LCM is 2 x 2 x 3 x 3 = 36. It extends to three or more numbers without changing. For 4, 6 and 15: 4 is 2 x 2, 6 is 2 x 3, 15 is 3 x 5, so the LCM is 2 x 2 x 3 x 5 = 60.
The GCD shortcut
For two numbers, the LCM equals their product divided by their greatest common divisor. Take 12 and 18: their GCD is 6, so 216 divided by 6 is 36. Take 21 and 55, which share no factors at all: the GCD is 1, so the LCM is just 1,155.
The reason it works is worth knowing. Every factor the two numbers share gets counted twice when you multiply them together, and dividing by the GCD removes the duplicate. That also explains the ceiling on the answer. The LCM of two numbers can never exceed their product, and it hits that product exactly when they share nothing. The shortcut only handles two numbers at a time, so for three you chain it: find the LCM of the first pair, then the LCM of that result and the third number.
Run your own numbers
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Open the Lcm CalculatorWhere you actually need one
Adding fractions is the obvious case. To add 3/8 and 5/12 you need a common denominator, and the smallest one available is the LCM of 8 and 12, which is 24. That gives 9/24 + 10/24 = 19/24, already in lowest terms. You could instead use 96, which is 8 x 12, and get 76/96, the same answer wearing a much bigger coat, and then you have to simplify it back down anyway.
Outside homework it is usually a scheduling question. Two buses leave the same stop at 9:00, one every 12 minutes and one every 18. When do they next leave together? The LCM of 12 and 18 is 36, so 9:36, and then every 36 minutes after that. The same arithmetic covers shift rotas, machine maintenance intervals and gear teeth returning to the same alignment.
It also tells you when repeating patterns collide. A job that runs every 4 days and one that runs every 6 land on the same day every 12 days, not every 24, which matters when you are trying to avoid the clash rather than schedule it.
How to use the LCM calculator
Enter two or more whole numbers separated by commas and read the result. Handling several at once is the main convenience, because it removes the chaining step, and the working is shown so you can check it rather than trusting it blind.
Two input rules. Use positive whole numbers, since the LCM is not defined in any useful way for fractions or negatives. And zero has no least common multiple with anything, because every multiple of zero is zero. If the LCM is a step towards a fraction problem rather than the answer itself, the fraction calculator guide covers what comes next.
Common questions
What is the LCM of 12 and 18? 36. Their GCD is 6, and 12 x 18 = 216, so 216 divided by 6 is 36. Nothing smaller than 36 divides evenly by both.
What is the difference between the LCM and the GCF? The GCF, also called the GCD, is the largest number that divides into both. The LCM is the smallest number both divide into. For 12 and 18, the GCF is 6 and the LCM is 36. One goes down from the numbers, the other goes up.
Can the LCM be smaller than the numbers? No. It is always at least as large as the biggest number in the set, and it equals that number when the largest is already a multiple of all the others. The LCM of 4 and 12 is 12.
What is the LCM of two prime numbers? Their product. Two different primes share no factors, so the GCD is 1 and the LCM of 7 and 11 is 77.