How HCF and LCM are explained by Cuemath students?



1. Introduction
2. Why learn HCF and LCM?
3. Let’s learn HCF
4. Let’s learn LCM
5. Conclusion
5. About Cuemath
6. Frequently Asked Questions (FAQs)
7. External references


19 November 2020

Reading time: 4 minutes


We at Cuemath believe that teaching math should be fun and exciting. 

We make complex concepts simple and intuitive through unique teaching methodology executed by our highly trained Cuemath teacher partners.

Have you wondered how Cuemath makes understanding math easy and logical?

If yes, you are in the right place. We will look at the concepts of HCF and LCM.  Cuemath students themselves will explain these concepts.

important notes to remember
"HCF and LCM are twin concepts and usually confusing to first-time learners."

You will get a firsthand account of how Cuemath makes learning easy with a logical approach to concepts and visualizations. 

You can also check out the above video to look at how our students are explaining these concepts.

Why learn HCF and LCM?

Cuemath believes that a student should know the ‘why’ behind a concept and not just ‘what’ of the concept. It makes the purpose of the lesson clear and understandable.

HCF and LCM are one of the most fundamental concepts in mathematics. A good understanding of these fundamentals helps students better understand the complex problems and topics they encounter in the future. 

important notes to remember
Good understanding of HCF and LCM helps students better understand the complex problems and topics they encounter in the future. 

HCF and LCM play a vital role in Number Theory. Topics like prime factorization, Permutation and combinations require absolute numerical rigor and can be a bit easier to understand if the fundamentals are clear.

HCF can be used in the following situations:

  1. When we want to split things into smaller sections.
  2. Arrange something in rows and groups

LCM can be used in the following situations:

  1. An event that is repeating over and over
  2. Figure out when something will happen again at the same time.

There are many more real-life and mathematical examples that you can find out for HCF and LCM. We have just mentioned some of them.

Let’s learn HCF

Hello, I am Thanas, and I am 10 years old. I am in Grade 5 at my school.

My hobbies are playing cricket and reading books. When I grow up, I want to go on a world tour and study in an IIT.

Today I am here to explain an important concept, which is How to find HCF. HCF stands for Highest Common Factor. To learn the Highest Common Factor, we should first understand what factors are.

important notes to remember
"Factors are the numbers that divide the given number equally."

We will learn factors using colorful fraction rods like below. If you want to read more about factors, Click Here


Let us arrange the above fraction rods in ascending order.


The white fraction rod is one unit. If we add one more white to it, it becomes two units.

Let us find the HCF of 4 and 6. To find it, first, you have to find the factors of 4 and 6 individually.


The factors of 4 are 1,2 and 4 itself because they all can divide 4.

The factors of 6 are 1,2,3 and 6 itself because they all divide 6.

3 cannot be a factor of 4 because 3 does not divide 4 equally. Similarly, 4 cannot be a factor of 6. Also, 6 cannot be a factor of 4 because it is greater than 4.

So, we find out that the common factor of 4 and 6 are 1 and 2. Here, 2 is greater than 1, So 2 is the ‘highest’ common factor for 4 and 6.

Congratulations, You have quickly learned about HCF. We do similar exercises for every concept at Cuemath.

Read more about HCF here.

Let’s learn LCM

Hello, I am Devansh, and I am 10 years old. I am in grade five at my school. My hobbies are playing cricket and football.

Let us learn the concept of LCM. LCM stands for Lowest Common Multiple. To understand LCM, we should know what a multiple is.

Multiple is a number that we get after multiplying some numbers with the given number. For example, If we multiply 5 with 2, we get 10. Hence, 10 is called a multiple of 5.

You can read more about multiples here. For today, let us find out the LCM of 4 and 6.

LCM of 4 & 6

Multiples of  4 are 4×1=4, 4×2=8, 4×3=12, 4×4=16, and so on.

Multiples of  6 are 6×1=6, 6×2=12, 6×3=18, and so on.

Many students are confused about why we only find the ‘Lowest Common Multiple’ and not the ‘Highest Common Multiple.’

The reason is that multiples are endless; you can always find a higher common multiple than the current one. So we cannot find the highest.

important notes to remember
The reason we only find the lowest common multiple and to the highest because multiples are endless, we can never find the highest. 

Coming back to the LCM of 4 and 6, we can observe that 43 is 12  and 62is also equal to 12. So the LCM of 4 and 6 turn out to be 12. 


Isn’t that easy? I learned this concept with the help of Cuemath’s Math box.

Read more about LCM here.


In the basic mathematics  H.C.F  and  L.C.M are an important concept related to factors or multiples of numbers. The calculation of H.C.F or L.C.M mainly focuses on the factorization  of given numbers into prime numbers.

  • The largest common factor of two or more numbers is called the highest common factor (HCF).
  • The smallest positive number that is a multiple of two or more numbers is called Lowest Common Multiple(LCM).

We hope that you got enough insights on HCF and LCM. At Cuemath, you lay strong emphasis on explaining math topics through visualizations and logical reasoning.

We have lots of such interactive videos and articles on other math topics that you can check out in our blog section.

About Cuemath

Cuemath, a student-friendly mathematics and coding platform, conducts regular Online Live Classes for academics and skill-development, and their Mental Math App, on both iOS and Android, is a one-stop solution for kids to develop multiple skills.Understand the Cuemath Fee structure and sign up for a free trial.

Frequently Asked Questions (FAQs)

1. How to find HCF?

HCF stands for Highest Common Factor. We calculate the factors of both the given numbers. The highest factor which divides them both equally is the HCF.

2. How to find LCM?

LCM stands for Lowest Common Multiple. We find the multiples of both numbers and then see the lowest multiple they have in common. This gives us the LCM.

3. How to enroll in Cuemath?

You can signup or login to Cuemath here and go through the various available programs. You can book a demo class to assess the classroom for yourself. Also, you can contact us for any further queries.

External references

To know more about HCF and LCM, visit these blogs

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