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Concise Mathematics Class 6 ICSE Solutions for Chapter 8 - HCF and LCM

ICSE

Concise Mathematics Class 6 ICSE Solutions for Chapter 8 - HCF and LCM

ICSE Class 6 Mathematics Chapter 8 Selina Concise Solutions - Free PDF Download

Selina Concise Mathematics Class 6 Solutions Chapter 8 are useful resources for students to follow during examinations. Students can frequently practice Selina Solutions to gain expertise in Mathematics. The answers provided here are well structured, as per the students’ understanding capacity in solving the questions with ease. Our subject experts have prepared these solutions to help students in scoring good marks in the final exams. Students who find difficulty while solving problems are advised to practice Selina's concise Maths Class 6 Solutions Chapter 8 effectively to boost confidence and face the exams without any fear.

Selina Concise Maths Class 6 Solutions Chapter 8 - Download Free PDF

Vedantu provides step-by-step solutions for Selina Concise Mathematics Class 6 Solutions Chapter 8. Students can download Selina concise maths class 6 solutions Chapter 8 Free PDF download option. All questions are solved and prepared by expert mathematics teachers as per ICSE board guidelines. The solution is provided in a step-by-step method that helps students in clearing their doubts, which appear while solving textbook questions.

Let’s have a look at the Concept of ICSE Mathematics class 6 Solutions Chapter 8

Prime Numbers: It is a natural number, which is divisible by only one, and itself is called a prime number.

Highest Common Factor: H.C.F. stands for Highest Common Factor. The H.C.F. of two or more given numbers is the greatest number (also known as a factor) which divides each given number completely.

Lowest Common Factor: L.C.M. stands for Lowest Common Multiple. The L.C.M. of two or more given numbers is the lowest (also known as smallest) number which is exactly divisible by each of the given numbers.

To find H.C.F. and L.C.M. of numbers we have two important methods that are the Prime factorization method and the division method. The shortcut method to find both H.C.F. and L.C.M. is a division method. We will also solve a few problems based on these two concepts to understand them better.

HCF and LCM Definition

HCF (Highest Common Factor)

The greatest common divisor or the gcd of two or more positive integers is the greatest positive integer that divides the numbers without leaving a remainder. For example, take 8 and 12. The H.C.F. of 8 and 12 will be 4 because the highest number that can divide both the numbers is 4.

LCM (Least Common Multiple)

The least common multiple or LCM of two numbers i.e a and b is denoted as LCM (a,b). The LCM is the smallest or least positive integer which is divisible by both the numbers. For example, Suppose two positive integers are 4 and 6.

Multiples of 4 are: 4,8,12,16,20,24…

Multiples of 6 are: 6,12,18,24….

As we can see, 12 is a common multiple. So, 12 is the LCM of 4 and 6.

List of HCF and LCM Properties

Property 1: The product of LCM and HCF of any two given natural numbers is equal to the product of those two given numbers.

Proof: Here, we need to prove LCM × HCF = Product of the Numbers

Suppose A and B are two numbers, then.

LCM (A and B) × HCF (A and B) = A × B

For example: If 3 and 8 are two numbers, and LCM (3, 8) = 24, HCF (3, 8) = 1

Sol: LCM (3, 8) x HCF (3, 8) = 24 x 1 = 24

Also, 3 x 8 = 24

Hence, proved.

Note: We can apply this property only for two numbers.

Property 2: HCF of co-prime numbers is 1. Therefore, the LCM of co-prime numbers is equal to the product of the numbers.

Proof: We need to prove LCM of Co-prime Numbers = Product of The Numbers.

For example: Let us take two coprime numbers, such as 21 and 22.

LCM of 21 and 22 = 462

Product of 21 and 22 = 462

LCM (21, 22) = 21 x 22

Property 3: H.C.F. and L.C.M. of Fractions:

LCM of fractions = (LCM of numerators)/(HCF of denominators)

HCF of fractions = (HCF of numerators)/(LCM of denominators)

For example: Let us take two fractions 4/9 and 6/21.

4 and 6 are the numerators whereas 9 and 12 are the denominators.

LCM (4, 6) = 12

HCF (4, 6) = 2

LCM (9, 21) = 63

HCF (9, 21) = 3

Now as per the formula, we can write:

LCM (4/9, 6/21) = 12/3 = 4

HCF (4/9, 6/21) = 2/63

Property 4: HCF of any two or more numbers will never be greater than the given numbers.

For example, the HCF of 4 and 8 is 4.

Here, one number is 4 and another number is 8 and HCF is also 4, which is greater than the HCF (4, 8).

Property 5: LCM of any two or more numbers will never be smaller than the given numbers.

For example, the LCM of 4 and 8 is 8 which is not smaller than any of them.

Solved Examples:

1. Prove that: LCM (9 and 12) × HCF (9 &=and 12) = Product of 9 and 12.

Ans: Given number is 9 and 12. We need to find factors 9 and 12.

Factor of 9 = 3 × 3 = 32

Factor of 12 = 2 × 2 × 3 = 22 × 3

LCM of 9 and 12 = 22 × 32 = 4 × 9 = 36

HCF of 9 and 12 = 3

We know that HCF and LCM of two numbers = Product of that numbers

LCM (9 and 12) × HCF (9 and 12) = 36 × 3 = 108

Product of 9 and 12 is 108

Hence, LCM (9 and 12) × HCF (9 and 12) = 9 × 12 = 108.

Hence Proved.

2. Find the highest common factor of 25, 35, and 45 by the prime factorisation method.

Ans: Given three numbers as 25, 35, and 45.

We know, 25 = 5 × 5

35 = 5 × 7

45 = 5 × 9

From the above expression, we can see 5 is the only common factor for all three numbers.

Therefore, the HCF of 25, 35, and 45 is 5.

Conclusion

Here we have discussed ICSE maths class 6 chapter 8 solutions. So, prime factorization is the process of breaking up a number into factors until only prime factors are left.

We have also learned that,

The Highest Common Factor (or HCF) of two or more given numbers is the highest common factor.

The Lowest Common Multiple (or LCM) of two or more given numbers is the lowest common multiples.

This solution is very important because we have covered all the important concepts of ICSE Mathematics Class 6 Solutions Chapter 8.

FAQs on Concise Mathematics Class 6 ICSE Solutions for Chapter 8 - HCF and LCM

1. How to download the Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 8 - HCF and LCM from the Vedantu website?

Students can go to the Vedantu website and type in Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 8 - HCF and LCM in the search box to get it. Alternatively, aspirants can get it by clicking on the Vedantu website. After you've opened the link, select "Download PDF" from the drop-down menu. On the website, you can also find a variety of ICSE test preparation materials. Students are urged to use a variety of study resources and learning aids in order to obtain the necessary amount of practice for passing the exam.

2. How do you prepare for the Class 6 ICSE Maths Exam?

The first and most important step in exam preparation is to study the Class 6 ICSE Maths Syllabus. Getting to know the syllabus provides a solid foundation for exam preparation. In addition, students in Class 6 will be able to become familiar with the exam pattern and the types of questions that will be asked. Students should also solve a lot of sample papers and worksheets before the exam to gain enough practice.

3. What are the benefits of practising Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 8 - HCF and LCM?

All Class 6 Maths students should practise Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 8 - HCF and LCM to learn the various strategies and formulas for answering problems quickly. These solutions also provide improved conceptual comprehension and knowledge of topics based on the comprehending capacity of the students. Solving textbook issues with these solutions aids pupils in achieving good exam scores. Furthermore, students can use the Concise Selina solutions to self-correct their answers and learn from their mistakes.

4. What types of Math resources are available on Vedantu the website for Class 6 ICSE Students?

Many maths materials are available on Vedantu, along with the essential conceptual explanations. The following are some of the free materials available to students at Vedantu:

Solutions for ICSE textbook and standard books
ICSE question papers and sample papers
The Lesson taught via interactive videos
Worksheets for maths
PDF-formatted lessons
Exam plans and syllabus
Important board exam questions
Notes for revision

5. What role does solving the Concise Mathematics book play in students' Class 6 exam preparation?

When students complete many question papers and test series, they will gain a better understanding of the exam's difficulty level, the topic-wise weightage, and the amount of effort required to pass the exam. While the questions asked in the Class 6 ICSE Maths are rarely repeated, the question and syllabus pattern of the examination remains consistent, therefore students should begin their preparation by solving and analyzing prior year question papers.

6. What are the Two Methods to Find HCF and LCM of a Number?

The two methods to find HCF and LCM of numbers are the Prime factorisation method and Division method.

7. Define LCM.

L.C.M. stands for Lowest Common Multiple. It is defined as the smallest positive number that is a multiple of two or more numbers.

8. Write is the Relation Between HCF, LCM, and Product of Two Natural Numbers.

The relation between HCF and LCM of two natural numbers is given below:

The product of H.C.F and L.C.M of two numbers = The product of given two numbers.