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.
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.
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.
"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.
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.
“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.
Conclusion
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.
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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.
