   Question Answers

# What is the H.C.F and L.C.M of fractions?  Hint: H.C.F full form is Highest Common Factor whereas L.C.M full form is Lowest Common Multiple. So factors are what we can multiply to get the number and multiples are what we get after multiplying the number by an integer.

Let’s take two fractions $\dfrac{a}{b}$ and $\dfrac{c}{d}$ .

To find H.C.F of $\dfrac{a}{b}$ and $\dfrac{c}{d}$ the generalized formula will be:

$\text{H}\text{.C}\text{.F}=\dfrac{\text{H}\text{.C}\text{.F of numerators}}{\text{L}\text{.C}\text{.M of denominators}}......(1)$

To find L.C.M of $\dfrac{a}{b}$ and $\dfrac{c}{d}$ the generalized formula will be:

$\text{L}\text{.C}\text{.M}=\dfrac{\text{L}\text{.C}\text{.M of numerators}}{\text{H}\text{.C}\text{.F of denominators}}......(2)$

Now L.C.M of two numbers is the smallest number (not zero) that is a multiple of both.

Now, to find out the LCM and HCF of fractions.

Let’s take the example of $\dfrac{2}{5}$ and $\dfrac{3}{7}$ .

As the numerators are (2,3) and denominators are (5,7) so now according to equation (1) we get,

$\text{H}\text{.C}\text{.F}=\dfrac{\text{H}\text{.C}\text{.F of (2,3)}}{\text{L}\text{.C}\text{.M of (5,7)}}........(3)$

So H.C.F of 2,3:

The factors of 2 are: 1, 2

The factors of 3 are: 1, 3

1 is the only common factor as it is the only number which is common to both 2 and 3.

Therefore, $\text{H}\text{.C}\text{.F of (2,3)}=1........(4)$

Now L.C.M of 5, 7:

The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, ....

The multiples of 7 are: 7, 14, 21, 28, 35, 42, ....

35 is the lowest common multiple as it is a multiple common to both 5 and 7.

Therefore, $\text{L}\text{.C}\text{.M of (5,7)}=35........(5)$

Putting value of H.C.F from equation (4) and value of L.C.M from equation (5) in equation (3)

we get, $\text{H}\text{.C}\text{.F=}\dfrac{1}{35}$ .

Now finding L.C.M for the same example,

$\text{L}\text{.C}\text{.M}=\dfrac{\text{L}\text{.C}\text{.M of (2,3)}}{\text{H}\text{.C}\text{.F of (5,7)}}........(6)$

So H.C.F of 5, 7:

The factors of 5 are: 1,5

The factors of 7 are: 1,7

1 is the only common factor as it is the only number which is common to both 5 and 7.

Therefore, $\text{H}\text{.C}\text{.F of (5,7)}=1........(7)$

Now L.C.M of 2, 3:

The multiples of 2 are: 2, 4, 6, 8, ....

The multiples of 3 are: 3, 6, 9, 12, ....

6 is the lowest common multiple as it is a multiple common to both 2 and 3.

Therefore, $\text{L}\text{.C}\text{.M of (2,3)}=6........(8)$

Putting value of H.C.F from equation (7) and value of L.C.M from equation (8) in equation (6)

we get, $\text{L}\text{.C}\text{.M=}\dfrac{6}{1}=6$ .

Note: Understanding the concept of H.C.F and L.C.M is the key here and chances of mistakes are when we in a hurry substitute L.C.M in place of H.C.F in equation (3) and equation (6) or we do vice-versa.
Application of LCM and HCF  Prime Factorization Of HCF And LCM  CBSE Class 7 Maths Chapter 2 - Fractions and Decimals Formulas  What is the full form of phd?  LCM Formula  What is the Difference Between Trade and Commerce?  What is Set, Types of Sets and Their Symbols?  What is Syphilis?  What is the Cell Envelope?  What is the Placebo Effect  Important Questions for CBSE Class 7 Maths Chapter 2 - Fractions and Decimals  Important Questions for CBSE Class 6 Social Science - Social and Political Life Chapter 3 - What is Government?  Important Questions for CBSE Class 7 English Honeycomb Chapter 10 - The Story of Cricket  Important Questions for CBSE Class 8 Science Chapter 10 - Reaching The Age of Adolescence  Important Questions for CBSE Class 6 Science Chapter 10 - Motion and Measurement of Distances  Important Questions for CBSE Class 6 Maths Chapter 7 - Fractions  Important Questions for CBSE Class 10 Maths Chapter 9 - Some Applications of Trigonometry  CBSE Class 8 Science Reaching The Age of Adolescence Worksheets  CBSE Class 8 Science Conservation of Plants and Animals Worksheets  Important Questions for CBSE Class 9 Maths Chapter 9 - Areas of Parallelograms and Triangles  Previous Year Question Paper of CBSE Class 10 English  CBSE Class 10 Maths Question Paper 2017  CBSE Class 10 Maths Question Paper 2020  Maths Question Paper for CBSE Class 10 - 2011  Maths Question Paper for CBSE Class 10 - 2008  Maths Question Paper for CBSE Class 10 - 2012  English Language and Literature Question Paper for CBSE Class 10 - 2011  Maths Question Paper for CBSE Class 10 (2016)  CBSE Class 10 English Language and Literature Question Paper with Solutions  English Language and Literature Question Paper for CBSE Class 10 - 2012  NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals  NCERT Solutions for Class 6 Maths Chapter 7  NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals In Hindi  NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals (EX 2.3) Exercise 2.3  NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals (EX 2.6) Exercise 2.6  NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals (EX 2.1) Exercise 2.1  NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals (EX 2.2) Exercise 2.2  NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals (EX 2.4) Exercise 2.4  NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals (EX 2.7) Exercise 2.7  NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals (EX 2.5) Exercise 2.5  