Are you finding it difficult to calculate the LCM of numbers? Are you confused about finding the LCM of two numbers, too? Don’t worry. Calculating LCM is easy when you understand it clearly. It is a simple yet most important topic in mathematics. LCM is used in school exams, competitive exams, and even in daily life. Learning how to calculate LCM easily with LCM techniques saves time, reduces errors, and boosts confidence in learning math.
In this blog, we will learn how to calculate LCM in easy steps and some quick LCM tricks to help us solve it faster without a math calculator.
Let’s get started.
Key Takeaways
- LCM (Least Common Multiple) is the smallest number that can be exactly divided by two or more numbers.
- It is essential in real life for syncing timings, scheduling, solving puzzles, and competitive exam questions.
- There are 3 major methods to calculate LCM:
- Listing Multiples
- Prime Factorization Method
- Division Method
- Vedic Maths tricks make LCM calculations faster and more efficient, especially for competitive exams.
- LCM is helpful in real-life situations such as traffic light intervals, medicine schedules, study timetables, and solving fractions in math.
- Know the differences between LCM and HCF methods to know the right method to solve the problem.
- When calculating LCM, students commonly make the following errors: stopping the calculation steps too early, missing some prime factors, or confusing or mixing up HCF and LCM methods.
- Students, parents, and teachers can master LCM at The Vedic Maths through guided video lessons, live classes, and practice worksheets.
- Regular practice and spotting patterns are key to solving LCM questions quickly and accurately.
- A free worksheet and demo class are available to boost your learning.
1. Introduction: Why Learning to Calculate LCM Is Essential
The Least Common Multiple (LCM) is a vital math idea that helps you solve many problems. You must calculate LCM when working with fractions, time schedules, patterns, financial planning, health or fitness calculations, or planning events. It’s a must-learn skill for school, exams, and daily life to perform math operations without a basic calculator.
However, many students find it difficult and sometimes even confused about finding the LCM. They are confused by the steps to calculate LCM or by the method to find LCM, which leads to mistakes and extra time in exams.
In this guide, you will learn:
- Easy methods to calculate LCM.
- Quick LCM tricks from Vedic Maths to solve problems faster.
- Learn to calculate the LCM easily with step-by-step examples and understand the concept clearly.
Let’s get started and learn LCM easily.
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3. What Is LCM?
The Least Common Multiple (LCM) is the smallest number that can be divided exactly by two or more given numbers.
In other words, the LCM is the first common multiple that can divide two or more numbers.
Let’s find the LCM of 11 and 13.
- Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143…
- Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143…
The first common multiple is 143.
So, the LCM of 11 and 13 is 143.
4. Why You Need to Calculate LCM in Real Life
The Least Common Multiple (LCM) is not just a classroom concept; it helps in many real-life situations where things repeat or need to match up exactly.
Let's see a few examples.
4.1 Everyday Examples
- Planning purchases: Suppose plates are sold in sets of 4 and cups in sets of 6. The LCM helps you figure out how many sets of each you need to buy so that every plate has a matching cup without any extras.
- Taking medicines on time: If you take one pill every 6 hours and another every 12 hours, LCM helps you know when to take them together.
- Managing transport or schedules: If two buses arrive at different time intervals, say every 15 minutes and every 20 minutes, LCM helps you find when they’ll come together next.
- Timing workouts: You do one exercise every 12 days and another every 18 days. LCM helps you plan when both fall on the same day.
4.2 Competitive Exam Applications
Competitive exams such as CAT, GRE, UPSC, SSC, Railways, and Banking, LCM questions were not asked directly; instead, real-life scenario problems were mentioned without mentioning the word "LCM".
For example,
- Bells tolling together
- Runners meeting at the starting point
- Traffic lights are changing at the same time
Why is the LCM important in competitive exams?
The above questions may look simple, but knowing how to calculate LCM quickly in a competitive exam where speed and time matter the most can save time and allow you to focus more on challenging problems.
Example question:
Three traffic lights change at intervals of 20 seconds, 30 seconds, and 40 seconds. If they all change at the same time now, after how many seconds will they change together again?
Solution:
We need to find the LCM of 20, 30, and 40.
- Prime factors:
- 20 = 2² × 5
- 30 = 2 × 3 × 5
- 40 = 2³ × 5
- LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120
Answer: The lights will change together again after 120 seconds.
5. How to Calculate LCM: Step-by-Step Methods
There are a few easy ways to calculate LCM. Let’s look at a few simple ways to find LCM with easy step-by-step examples.
5.1 Listing Multiples:
This is the simplest listing method; it works best when the numbers are small, but it’s slow for larger numbers.
How it works:
- Step 1: Write the list of multiples for each number.
- Step 2: Look for the smallest multiple that appears in both lists.
For Example,
Let’s calculate the LCM of 2 and 3 using the listing multiples method:
Step 1: Write down the list of multiples.
- Multiples of 2: 2, 4, 6, 8, 10...
- Multiples of 3: 3, 6, 9, 12, 15..
Step 2: Look for the lowest multiple in both lists.
The lowest common multiple is 6.
LCM of 2 and 3 = 6.
5.2 Prime Factorization:
This is the fastest method, especially for larger numbers.
How it works:
- Step 1: Break each number into its common prime factors.
- Step 2: List all the prime numbers that appear, using the highest power of each.
- Step 3: Multiply them together to get the LCM.
For Example,
Let’s calculate the LCM of 12 and 16 using the prime factorisation method:
Step 1: Find each number's common Prime factors (exponent form):
- 12 = 2² × 3
- 16 = 2⁴
Step 2: Take the highest powers of each prime:
- 2⁴ (from 16)
- 3 (from 12)
Step 3: Multiplying the highest powers together
LCM = 2⁴ × 3 = 16 × 3 = 48
5.3 Division Method:
This is the most common method taught in schools. It’s great for calculating two or more numbers at once. It is also called as cake method or ladded method.
How it works:
- Step 1: Write the numbers side-by-side.
- Step 2: Divide by any prime number that fits at least one of them.
- Step 3: Keep dividing until no more common factors are left.
- Step 4: Multiply all divisors and remaining numbers to get the LCM.
For Example,
Let’s calculate the LCM of 8 and 12 using the division method:
Step 1: Write numbers side-by-side
- 8 12
Step 2: First, we divide by the prime number 2, which gives us 4 and 6. We can divide by 2 again, which leaves us with 2 and 3, and divide again, which gives us 1 and 3.
- 2 | 8 12
- 2 | 4 6
- 2 | 2 3
- 1 3
Step 4: Multiply all divisors and remaining numbers
LCM = 2 × 2 × 2 × 1 × 3 = 24
The least common multiple of 8 and 12 is 24.
6. LCM Tricks: How to Calculate LCM Faster
Want to solve LCM problems faster?
These easy tricks will help you save time, improve number theory especially in school exams, competitive exams, or when you need quick answers.
6.1 Shortcut Patterns
Here are some quick rules that work like magic:
- Rule 1: If one number is a multiple of the other
For Example,
- LCM of 3 and 12
Since 12 is already a multiple of 3,
LCM = 12
- Rule 2: If the numbers are prime (no common factors except 1)
For Example,
- LCM of 3 and 5
No common factors, so
LCM = 3 × 5= 15
- Rule 3: LCM of even and odd numbers
For Example,
- LCM of 2 and 7
No common factors,
LCM = 2 × 7 = 14
6.2 Vedic Maths Tips for Speed
Vedic Maths makes LCM faster using pattern recognition mentally.
Let’s see how vedic maths is better than traditional maths.
Example: Find the LCM of 12 and 18
Traditional Method (Prime Factorisation method):
- Step 1: 12 = 2² × 3
- Step 2: 18 = 2 × 3²
- Step 3: LCM = 2² × 3² = 4 × 9 = 36
Vedic Maths Method:
See that both numbers share 3 as a common factor.
- Step 1: Multiply the highest powers mentally:
2² (from 12), 3² (from 18)
Directly get 36; no factor trees are needed
Easy right?
With Vedic Maths, you don’t just memorize; you understand the pattern, making you calculate 10× faster.
Want to learn more Vedic Maths tricks?
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7. Calculate LCM of 2, 3, or More Numbers
Finding the LCM of more than two numbers is very easy in just a few steps
7.1 Step-by-Step Examples (Using the Division Method)
Let’s find the LCM of 4, 6, and 8 using the Division Method (also called the cake/ladder method):
We divide all numbers at once by common prime numbers until we are left with only 1s.
2 | 4 6 8
---------
2 3 4
2 | 2 3 4
---------
1 3 2
2 | 1 3 2
---------
1 3 1
3 | 1 3 1
--------
1 1 1
Now multiply all the divisors on the left:
LCM = 2 × 2 × 2 × 3 = 24
LCM of 4,6, and 8 is 24
7.2 Common Mistakes to Avoid:
Here are some Common Mistakes to avoid when calculating LCM with a quick fix.
| Don't do this | Do this instead |
|---|---|
| Confused with LCM and HCF | LCM is always equal to or greater than the numbers. HCF is equal to or less. |
| Stop dividing when one number becomes 1 | Keep dividing until all numbers become 1 |
| Miss out on a prime factor | Double-check that all prime factors are used completely. |
| Think LCM must be a factor | Remember, LCM is a multiple, not a factor |
8. LCM vs HCF: Understanding the Difference
| Feature | LCM (Least Common Multiple) | HCF (Highest Common Factor) |
|---|---|---|
| Meaning | The smallest number that is a multiple of two or more numbers. | The largest number that divides two or more numbers exactly. |
| that Also Known As | Lowest Common Multiples | Greatest Common Divisor (GCD) |
| Value Range | Always equal to or greater than the given numbers. | Always equal to or less than the given numbers. |
| Use Case | Used when adding or subtracting fractions, finding timings, or syncing cycles. | Used to simplify fractions or divide items into equal parts. |
| Example | LCM of 4 and 6 = 12 | HCF of 4 and 6 = 2 |
| Real-Life Application | Finding the first time events happen together (e.g., traffic lights). | Splitting something into the largest equal parts (e.g., cutting rope). |
| Mathematical Operation | Based on multiples | Based on Factors |
9. Practice with LCM Worksheets & Quizzes (Included in Our Courses)
With practice, one can master the skills required to calculate LCM. That's why we created the Vedic Maths Bundle Kit and Live Classes. Worksheets and quizzes are part of our learning kits. Clarify your doubts with expert Mamta Rupesh, who has trained 15,000+ students, 5,000+ Parents, and Teachers.
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10. Real-Life Student Success Stories with Vedic Maths LCM Learning
See how our students transformed their math skills with our Vedic Maths courses.
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11. Conclusion: Master LCM, Master Speed
The Least Common Multiple (LCM) is not just a math topic; it’s a powerful skill that helps you solve problems in school, exams, and daily life.
While traditional mathematical methods are helpful, Vedic Maths tricks give you a big advantage, especially when speed and accuracy matter most, like in competitive exams or time complexity tests.
With Vedic Maths, you don’t just learn the steps. You understand the patterns. That’s how you solve LCM problems faster, easier, and more confidently.
At Vedic Maths, we make learning fun and simple for everyone. Students, parents, and teachers, you’ll learn faster ways, clear steps, and avoid the usual mistakes.
What You Can Do Next:
- Download FREE LCM Worksheet with 20 practice problems and answers.
- Book a Free Demo Class to learn more Vedic Maths tricks with expert Mamta Rupesh.
- Explore our Vedic Maths Course Kit with videos, quizzes, and easy practice tools.
Let’s make LCM one of your strongest math skills.
Simple learning. Fast results. More confidence.
11. FAQs on Calculating LCM
1What is the easiest way to find the LCM?
The easiest method for small numbers is the Listing the Multiples method. Use the Prime Factorization Method or Division Method for bigger numbers, and try Vedic Maths tricks for speed.
2Can the LCM be one of the numbers itself?
Yes, if one number is a multiple of the other.
For example, the LCM of 3 and 6 is 6.
3What’s the LCM of two prime numbers?
If both numbers are prime (like 2 and 5), or co-prime numbers then their LCM is just the product of prime numbers.
LCM of 2 and 5 = 2 × 5 = 10
4What’s the fastest way to find the LCM of large numbers?
Use the Vedic Maths method or Prime Factorization. These methods help you skip long steps and reach the answer quickly without any LCM formula, and can be used in exams and mental math calculations.
5What’s the difference between LCM and HCF?
LCM ( Least Common Multiple) is the smallest number that both can divide into.
HCF (Highest Common Factor) is the biggest number that divides both.
Example:
- LCM of 4 and 6 = 12
- HCF of 4 and 6 = 2
6Why do we need to learn LCM in real life?
LCM helps in everyday tasks, like syncing time schedules, planning events, or taking medicines on time. It’s also important for competitive exams and understanding patterns.
7Can I find the LCM of more than two numbers?
Yes. You can find the LCM of two numbers at a time and then use that result to find the LCM of the next number.
8Is LCM important for competitive exams?
Absolutely. LCM appears in questions about timings, bells ringing, traffic lights, or runners meeting. It often shows up disguised, and solving it quickly saves time.
9Can LCM ever be smaller than both numbers?
No. The LCM is always equal to or greater than the largest number in the group.
10How can I get better at solving LCM problems?
- Practice regularly using methods like listing the multiples, prime factorization, and Vedic Maths tricks. Focus on patterns, avoid common mistakes, and stay consistent.
