Ch- 6 MATHEMATICS H.C.F & L.C.M

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Chapter- 6 (H.C.F & L.C.M)

H.C.F means- Highest Common Factor. 

For Practice at Home

First Method- With the help of Multiplication tables (By Inspection) 

इसे हम कहानी से समझते है | इस कहानी में दो लोग है - भाई और बहन | भाई का नाम अर्थ है और बहन का नाम रिया है |

रिया- भाई, आपको tables आती हैं?

अर्थ - हाँ जी, क्यों नहीं |

रिया - तो बताओ 12 और 8  दोनों किस-किस की tables में आते  है ?

अर्थ-   1, 2 और  4  की |

रिया - भाई क्या आपको पता है- 1, 2 and 4 are the common factors of 12 and 8.

अर्थ - यस , लेकिन H.C.F तो बताओ, यह क्या होता है ?

रिया- H.C.F means Highest Common Factor. 

         Now can you tell me Highest Common factor among these common factors-

                                  1,   2,   4 

अर्थ- यस, 4. 

रिया-  Correct.

Arth- अब समझ आया कि 12 और 8 का Highest Common Factor (H.C.F) 4 है |

रिया - चलो, अब बाकी parts करो |

 

Exercise 6 A

Method- 

1    a) 3 and 6

          We know that both 3 and 6 are in the tables of 1 and 3.

          Among these 3 is the highest number.

          So H.C.F of 3 and 6 is 3.

      c) 18 and 27

          We know that both 18 and 27 are in the tables of 1, 3 and 9.

          Among these 9 is the highest number.

          So H.C.F of 18 and 27 is 9.

      2 a) 33 and 44

          We know that both 33 and 44 are in the tables of 1 and 11.

          Among these 11 is the highest number.

          So H.C.F of 33 and 44 is 11.

      2 c) 15 and 25

           We know that both 15 and 25 are in the tables of 1, 5.

          Among these 5 is the highest number.

          So H.C.F of 15 and 25 is 5.

       2 d) 24 and 36

           We know that both 24 and 36 are in the tables of 1, 2, 3, 4, 6, 12.

          Among these 12 is the highest number.

          So H.C.F of 24 and 36 is 12.

Second Method-  With the help of Finding Factors

रिया- अब हम Question 4C लेते है, 

          20 और  32. 

         अब बताओ कि 20 किस -किस की tables में आता है ?

अर्थ- 1, 2, 4, 5, 10 and 20.

         हाँ, याद  आया, 

रिया- What?

अर्थ- These are the factors of 20.

 Riya- Can you tell me the factors of 32?

Arth- Oh yes, 32 comes in the tables of 1, 2, 4, 8, 16 and 32. So these are the factors of 32.

Riya- So, Look at the following Solution

4 c ) Factors of 20                                      = 1, 2, 4, 5,10, 20

Factors of 32                                              = 1, 2, 4, 8, 16, 32

Common factors of 20 and 32           = 1, 2, 4 

Highest Common Factors(H.C.F)     = 4

  

रिया- Now you will do rest of the parts.

अर्थ- हाँ दीदी , Thank you.

4 a)  6 and 9

         Factors of 6                  = 1, 2, 3, 6

         Factors of 9                  = 1, 3, 9

         Common factors of 6 and 9 = 1, 3

         Highest Common Factors (H.C.F) = 3

4 b)   10 and 15

         Factors of 10                  = 1, 2, 5, 10

         Factors of 15                  = 1, 3, 5, 15

         Common factors of 10 and 15 = 1, 5

         Highest Common Factors (H.C.F) = 5

Third Method-  By Prime Factorisation

Arth- Sister, Can you tell me the third method?

Riya- Look the following solution, -

                                             

                                                         

                                                                                                                                                        

           

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More Sums for Practice...........these will not be done in Copy..

Exercise 6 B

See above questions carefully, in these questions we have to find out numbers by which, these given number should be completely divisible without leaving any remainder. It means the number will be Common Factor of the given numbers. 

Here we will find out Highest Common Factors of these given numbers by the third method                          

                                           "Prime Factorisation".   

Lets start- 

As we have learned,

 How to find out H.C.F by prime factorisation method.

We take only common factors to get H.C.F.

Exercise 6C

रिया - भैया, सुना है कि फिर से ऑनलाइन क्लासेज शुरू हो रहीं हैं |

अर्थ- हाँ, दीदी | पर आपने LCM निकलना नहीं सिखाया |

रिया - आज मैं आपको सीखती हूँ | 3 और 4 का LCM निकालते हैं |

         अब  3 और 4 का टेबल सुनाओ |

अर्थ - 3, 6, 9, 12, 15, 18, 21, 24, 27, 30................................

         4, 8, 12, 16, 20, 24, 28, 32, 36, 40..............................

रिया-  Please say, Common Multiples of 3 and 4.

Arth- 12 and 24.

Riya- L.C.M means Lowest Common Multiple. (सबसे छोटा )

अर्थ-  12 

रिया - Correct. So L.C.M of 3 and 4 is 12. 

Multiplication Tables Method.

Q.1(a).    3 and 6

The multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

The multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Common multiples of 3 and 6 = 6, 12, 18, 24, 30

So L.C.M of 3 and 6 = 6

Q.1(b).    4 and 8

The multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

The multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

Common multiples of 4 and 8 = 8, 16, 24, 32, 40

So L.C.M of 4 and 8 = 8

Q.2(a).    9 and 15

The multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

The multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150

Common multiples of 9 and 15 = 45, 90

So L.C.M of 9 and 15 = 45

Q.2(b).    12 and 16

The multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120

The multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160

Common multiples of 12 and 16 = 48, 96

So L.C.M of 12 and 16 = 48

Inspection Method-

This  is direct method. 

Lets find out L.C.M of 4, 6 and 9.

Q.3 c)         4, 6 and 9

We know that 36 is in the tables of 4, 6 and 9.

36 is the Lowest Common Multiple of 4, 6 and 9.

So L.C.M of 4, 6 and 9 = 36  

Q3d)   8, 9, 12

We know that 72 is in the tables of 8, 9 and 12.

72 is the Lowest Common Multiple of 8, 9 and 12.

So L.C.M of 8, 9 and 12 = 72  

Exercise 6D 

Finding L.C.M by Prime factorisation Method

Now we will take rest of all factors with common factors to get L.C.M.

             

 

Exercise 6 E

More Sums for Practice...........these will not be done in Copy..