Struggling with math homework or trying to add fractions with different denominators? You’ve probably come across the term “LCM.” If you’ve ever had to calculate LCM, you know it can sometimes be a tricky process. But what is LCM?
LCM stands for Least Common Multiple. It’s a fundamental concept in math, and understanding it is key to solving many problems.
While there are several manual ways to find it, the fastest and most reliable method is using our free LCM Calculator. This article will guide you through everything you need to know, from the basic definition to the manual methods, and show you how our tool can make your life easier.
What is LCM?
So, what is a LCM? The Least Common Multiple (LCM) of two or more numbers is the smallest positive number that is a multiple of all the numbers in the set.
For example, to find the LCM of 4 and 6, you would list their multiples:
- Multiples of 4: 4, 8, 12, 16, 20, 24…
- Multiples of 6: 6, 12, 18, 24, 30…
The common multiples are 12, 24, and so on. The least (smallest) of these common multiples is 12. Therefore, the LCM of 4 and 6 is 12.
You might ask, what is an LCM used for? The most common use is when you need to add or subtract fractions. You must find a “common denominator” to make the calculation possible, and the LCM is the least common denominator.
Manual Methods: How to Calculate LCM
If you want to learn how to find the LCM by hand, there are three popular methods. We’ll show you how to get LCM step-by-step using each one.
Method 1: Listing Multiples
This is the method we used above. It’s the simplest but can be slow for large numbers.
- List the multiples of each number.
- Find the first multiple that appears in all lists.
- That number is the LCM.
Method 2: Prime Factorization
This is a very reliable way for how find lcm, especially for bigger numbers.
- Find the prime factorization of each number (break it down into only prime numbers).
- List all the prime factors that appear in any of the factorizations.
- For each prime factor, find the highest power it appears in any one factorization.
- Multiply these highest powers together to get the LCM.
Method 3: The Division Method (Ladder Method)
Many people prefer this visual way for how to take lcm.
- Write your numbers in a row.
- Divide them by the smallest prime number that divides at least one of them.
- Write the quotients (the results) and any undivided numbers in a new row below.
- Repeat the process until all the numbers in the bottom row are “1”.
- Multiply all the prime numbers you used to divide (the numbers on the left) to get the LCM.
Examples: How to Find the LCM
Let’s use those manual methods to answer the most common questions people ask.
What is the LCM of 8 and 12?
This is the same question as what is the lcm of 12 and 8 or what are the lcm of 8 and 12.
- Using Prime Factorization:
- $8 = 2 \times 2 \times 2 = 2^3$
- $12 = 2 \times 2 \times 3 = 2^2 \times 3^1$
- The highest power of 2 is $2^3$. The highest power of 3 is $3^1$.
- LCM = $2^3 \times 3^1 = 8 \times 3 = \mathbf{24}$
What is the LCM of 6 and 10?
- Using Listing Multiples:
- Multiples of 6: 6, 12, 18, 24, 30, 36…
- Multiples of 10: 10, 20, 30, 40…
- LCM = $\mathbf{30}$
What is the LCM of 9 and 12?
- Using the Division Method:
- $2 \mid 9, 12$
- $2 \mid 9, 6$
- $3 \mid 9, 3$
- $3 \mid 3, 1$
- $\phantom{3} \mid 1, 1$
- LCM = $2 \times 2 \times 3 \times 3 = \mathbf{36}$
What is the LCM of 4 and 6?
- Using Listing Multiples:
- Multiples of 4: 4, 8, 12…
- Multiples of 6: 6, 12…
- LCM = $\mathbf{12}$
What is the LCM of 8 and 10?
- Using Prime Factorization:
- $8 = 2 \times 2 \times 2 = 2^3$
- $10 = 2 \times 5$
- Highest power of 2 is $2^3$. Highest power of 5 is $5^1$.
- LCM = $2^3 \times 5 = 8 \times 5 = \mathbf{40}$
The Fastest Way: Use Our Free LCM Calculator
Learning the manual methods is great for school, but in the real world, you just need the answer fast.
Our LCM Calculator is the best tool for the job. You don’t have to worry about how to calculate LCM by hand, list multiples, or make a mistake with prime factors.
How to use our calculator:
- Go to our LCM Calculator page.
- Enter the numbers you want to find the LCM for (e.g., 8, 12).
- Click “Calculate.”
- The tool instantly gives you the correct LCM.
It’s fast, accurate, and works for any set of numbers, including three or more!
LCM FAQs
Q: What is LCM in math?
LCM stands for Least Common Multiple. It is the smallest positive number that is a multiple of two or more given numbers.
Q: How find lcm quickly?
The absolute fastest and most accurate way is to use our LCM Calculator. Just type in your numbers, and you’ll get the answer instantly.
Q: How to take LCM of three numbers?
You can use the same manual methods (prime factorization or division method) for three or more numbers. Or, for a much easier way, simply enter all three numbers into our LCM Calculator.
Q: What’s the difference between LCM and HCF (or GCF)?
LCM (Least Common Multiple) is the smallest number that your numbers divide into. HCF (Highest Common Factor) or GCF (Greatest Common Factor) is the largest number that divides into your numbers. They are opposites.