New Elementary Mathematics, Syllabus D-1, Chapter 1

Class Std.-VI
New Elementary Mathematics Syllabus D-1
Chapter 1

Exercise 1.5 Page- 13

Problem 1: Find the Highest Common Factor of 60 and 96.                                                                            
Solution:      Consider the numbers 60 and 96
The list of factors of 60 is 1, 2 , 3 , 4 , 5 , 6 , 10 ,12 , 15 , 20 ,30 and 60
The list of factors of 96 is 1, 2 , 3 , 4 , 6 , 8 ,12 , 16 , 24 ,32 , 48 and 96
The list of all the common factors of 60 and 96 is 1, 2 , 3 , 4, 6 and 12
Therefore the largest of these common factors is 12 and thus we call 12 the Highest Common Factors (H C F) of 60 and 96

Another method:  The list of all factors of 60 = 2 × 2 × 3 × 5  and
                                                                                96 = 2 × 2 × 2 × 2 × 2 × 3  
                                                     Therefore   H C F = 2 × 2 × 3 = 12  Ans.

Problem 2: Find H C F of 36 , 24 , 144 , and 96 .

Solution:  The list of factor of  36 = 2 × 2 × 3 × 3
                                                          24 = 2 × 2 × 2 × 3
                                                         144 = 2 × 2 × 2 × 2 × 3 × 3
                                                           96 = 2 × 2 × 2 × 2 × 2 × 3
Therefore the H C F is = 2 × 2 × 3 = 12  Ans.

Exercise 1.6 Page- 16

Problem 1: Find the Least Common Multiple(LCM) of 12 and 18.                                                                                                                                                                              
Solution: Consider the numbers 12 and 18
The list of all multiples of 12 is 12, 24 , 36 , 48 , 60 ,72 ……
The list of all multiples of 18 is 18 , 36 , 54 , 72 , 108 ………
The list of all the common multiples of 12 and 18 is 36 and 72 ……
Therefore the smallest of these common multiples is 36 and thus we call 36 the Least Common multiples (LCM) of 12 and 18

Another method:  The list of all factors of 12 = 2 × 2 × 3  and
                                                                                       18 = 2 × 3 × 3 
                                             Therefore L C M = 2 × 2 × 3 × 3 = 36 Ans

Problem 2: Find the Least Common Multiple (LCM) of 24, 18 and 36

Solution:  The list of all factors of  24 = 2 × 2 × 2 × 3 
                                                                    18 = 2 × 3 × 3 
                                                                    36 = 2 × 2 × 3 × 3
            Therefore   L C M = 2 × 2 × 2 × 3 × 3 = 72 Ans

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