LCM Calculator

Least Common Multiple Calculator: Find the LCM Instantly

Enter the numbers in least common multiple calculator you want to find the least common multiple of and press “calculate.” You’ll get the answer and the whole process, not just a number, so you can use the steps in your schoolwork and really understand them. It can deal with two numbers or twenty. There are three common ways to find the LCM by hand, which are shown below the tool. 

It is different from other pages because all of the ways to solve the LCM of 12 and 18 are the same. The fastest way to see how they connect is to watch three different paths lead to the same answer. You can then choose the one your teacher wants.

What Is the Least Common Multiple?

The least common multiple calculator calculates, for two numbers the smallest number that both of them can be split into.

That sounds vague, so watch what happens with 4 and 6.

Fours: 4, 8, 12, 16, 20, and 24 Six times a number: 6, 12, 18, 24

There are 12 on both lists. Both lists also have 24 on them. The least frequent number is 12, though, because it comes first.

The LCM of 4 and 6 is 12.

When you multiply a number by 1, 2, 3, and so on, you get a multiple. A number that appears in both lists is called a common multiple. The least common multiple is the one that they both have the least of.

A word about names. It’s known as the least common multiple in the US. Most textbooks in the UK, Australia, and Canada use the term “lowest common multiple.” The answer is the same, but the word is different. Everything on this page is useful if your worksheet asks you to find the smallest number that both numbers can be multiplied by.

You will also see this tool, which is also known as an LCM calc, or least common multiple calculator. Those are also the same tool.

How to Find the Lowest Common Multiple of Two Numbers

One of the three standard methods is likely what your textbook tells you. All three are right. Some cases call for one and not the other.

1. The first thing you learn is how to calculate LCM.
2. The prime factorization is the one that doesn’t break down.
3. If you already know the GCF, the GCF route is the fastest way to get there.

All three parts below solve the same problem: find the LCM of 12 and 18. This shows that they all agree. All three routes lead to the same answer.

Method 1: Listing Multiples (Best for Small Numbers)

This is the exact method that fits the definition. Make two lists and look for the first one that matches.

Step 1: Write down all the numbers that are divisible by 12: 12, 24, 36, 48, and 60.

Step 2: Write down all the numbers that are divisible by 18: 18, 36, 54, and 72.

Step 3. Do it. Find the list’s first number. 36 shows up in both. Smaller doesn’t do anything.

The square root of 12 and 18 is 6.

You can save time by only writing out multiples of the bigger number. Then, check each one to see if it can be divided by the smaller number. Start with 18. Twelve does not split 18. Next, number 36. How do you divide 12 by 36? Three times, yes. It only took two steps instead of nine.

This method doesn’t work when you use it on 48 and 180. It would take a long time to write multiples before they meet at 720. As soon as your numbers go over 20, switch to one of these ways. This is another reason why mistakes happen with long lists. If you make a mistake in the 7 times table, your whole answer is wrong.

Method 2: Prime Factorization (Best for Large Numbers)

This is the way to do it for any number, no matter how big it is. There are a few more steps, but you’ll never have to write out a million lists.

First, separate both numbers into primes. Then, find the prime that shows up most often in both numbers.

Step 1: Split 12 up into primes. 12 = 2 × 2 × 3, which we write as 2² × 3.

Step 2: Split 18 up into primes. 18 = 2 + 3 + 3, which we write as 2 + 3².

Step 3: For each prime, pick the bigger number.

Step 4: Take four times what you took. 2² times 3² is 4, and 4 times 9 is 36. LCM(12, 18) is 36. The answer is the same as in Method 1.

How “the most times it appears” gets the job done. To be able to divide by 12, the LCM on the least common multiple calculator must have at least two 2s. Also, it must be divisible by 18, which means it needs at least two 3s. Taking the bigger requirement for each prime gives you the smallest number that meets both of them. If you take any less, one of them won’t split in half.

You can use our prime factorization tool to see the whole tree if you need help breaking numbers down into primes.

Method 3: The GCF/HCF Shortcut (Fastest for Two Numbers)

This only takes ten seconds if you already know the biggest thing they have in common.

LCM(a, b) = (a × b) ÷ GCF(a, b)

Step 1: Figure out the GCF of 12 and 18. One, two, three, four, six, twelve 18 parts: 1, 2, 3, 6, 9, 18 Six is the largest number on both lists.

Step 2. Take the two numbers and multiply them. 12 times 18 is 216.

Third Step: Divide by the GCF. 216 ÷ 6 = 36 LCM(12, 18) = 36. Three ways to do something, three different paths, one answer. That’s not luck. It shows that both ways of talking about it are correct.

What is it? US textbooks say GCF, which stands for “greatest common factor.” In texts from the UK and Australia, HCF stands for “highest common factor.” The formula works both ways because they both mean the same number. LCM(a, b) = (a × b) ÷ HCF(a, b) if that’s how your class writes it.

The shortcut has one useful shortcut inside it. Both the GCF and LCM are 1. The GCF is 1, and the LCM is just the product of the two numbers found with the help of the least common multiple calculator. It’s easy to see that LCM(7, 9) = 7 × 9 = 63.

Need the GCF first? It only takes one step for our GCF and HCF calculator to find it.

Which Method Should You Use? (Or Just Use the LCM Calculator)

A word of caution about the GCF method. You can only use two numbers with it. A lot of the time, students try to make it three, like this:

(4 times 6 times 10) times GCF(4, 6, 10) times 2 = 120

That answer isn’t right. The next part shows that the least common multiple calculator will help you to find the real LCM of 4, 6, and 10 is 60. When there are three or more numbers, use prime factorization.

Use the method your teacher taught you and show how you worked on a test. For real life, use the number pad at the top of this page.

Finding the LCM of Three or More Numbers

Prime factorization handles this cleanly. Nothing new to learn you just add a column.

Worked example: LCM(4, 6, 10)

Step 1. Break each number into primes. 4 = 2² 6 = 2 × 3 10 = 2 × 5

Step 2. For each prime, take the highest power anywhere in the list.

Step 3. Multiply. 2² × 3 × 5 = 4 × 3 × 5 = 60

LCM(4, 6, 10) = 60 

Always check. Divide 60 by each of your original numbers and make sure there is no remainder. 60 ÷ 4 = 15. 60 ÷ 6 = 10.

Where the Least Common Multiple Is Actually Used

Adding fractions. This is the important one. To add 1/12 and 1/18, you need to find the smallest number that they both equal. The LCM gives you that number. Since LCM(12, 18) = 36, the answer is 5/36, which is 336 + 236. This is done immediately by our fraction calculator.

Scheduling repeating events. Each bus leaves at the same time from the same stop. One comes back every 12 minutes, and the other every 18 minutes. When are they going to get there again together? 12 x 18 = 36 minutes is the LCM.

Gears and patterns. There are two gears with 12 and 18 teeth. After 36 teeth have gone through, they both go back to where they started. Traffic light cycles and tile patterns that repeat work the same way.

Check Your Homework With the Least Common Multiple Calculator

First, do the problem by hand. Then, type it into the box at the top of this page. You know your method works if your answer is the same. If it doesn’t, the working panel shows each step, so you can see where you went wrong instead of just seeing a different number.

Remember these two things. Most teachers grade not only the answer but also the work that went into it, so copy the steps instead of the answer. Also, if your class uses HCF instead of GCF, change the wording toggle to match what’s in your textbook.

FAQs

Q1. How do you find the LCM of two numbers?

There are three right ways to do it. Write down all the numbers that are multiples of each other and pick the first one that they both share. Or, separate them into primes and find the prime that shows up most often in each. You can also use LCM(a, b) = (a × b) ÷ GCF(a, b). As you can see from the examples above, all three give LCM(12, 18) = 36.

Q2. What is the difference between LCM and GCF (or HCF)?

They pull away from each other. The GCF is less than your numbers because it is the biggest number that can be split in half. Both of your numbers can be divided into the LCM, so it is bigger than your numbers. The GCF of 12 and 18 is 6, and the LCM is 36.

Q3. Is ‘lowest common multiple’ the same as ‘least common multiple’?

Yes, it’s the same. “In the US, “least common multiple” is the standard term. In the UK, Australia, and Canada, “lowest common multiple” is the standard term. They both shorten to LCM and give the same answer. Both GCF and HCF are split up by region in the same way.

Q4. How do I find the LCM of three numbers?

Make use of prime factorization. Sort each number into primes, then find the largest power of each prime that shows up anywhere in the list. For 4, 6, and 10, 4 = 2², 6 = 2 × 3, and 10 = 2 × 5. This means that you need to take 2², 3, and 5 to get 60. There is only one GCF trick that will work here, so don’t use it.

Q5. Can the LCM ever be smaller than the largest number?

No, never. There can only be one LCM for each number you started with, and the smallest number that can be an LCM of any other number is itself. So the least common multiple calculator is always give at least the biggest number you put in. When the biggest number divides evenly into all the other numbers, it equals that biggest number. For example, LCM(4, 12) = 12.

Q6. Why do I need the LCM for adding fractions?

There is only a way to add fractions when the numbers at the bottom match. The smallest common denominator is found by taking the LCM of the denominators. This makes the numbers manageable and usually means you don’t have to simplify them as much at the end. To get 5/36 from 1/12 + 1/18, you write them as 3/36 and 2/36, since the LCM of 12 and 18 is 36.

Conclusion

One answer, three ways. It’s easy to list multiples, and it works fine for small numbers too. Prime factorization has a few more steps, but it never breaks down. This is why it is best for big numbers and amounts of three or more. If there are only two numbers and you already know the GCF, the GCF method is the fastest. The point of this page is to see that all three of them gave 36 for LCM(12, 18). Choose the calculator your class uses and do the work by hand. Then, before the test, compare your work to the least common multiple calculator at the top to make sure you got it right.