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Real Numbers
Question
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In a morning walk Nimit, Tanvika and Mehul step off together, their steps measure 84 cm, 90 cm and 120 cm respectively. What is the minimum distance each should walk so that one can cover the distance in complete steps.

Answer

 Required distance is the LCM of 84 cm, 90 cm and 120 cm.

Thus,

Since, 84 = 2 × 2 × 3 × 7 = 22 × 3 × 7

90 = 2 × 3 × 3 × 5 = 2 × 32 × 5

and    120 = 2 × 2 × 2 × 3 × 5

= 23 × 3 × 5

∴ LCM = Product of each prime factor with highest power

= 23 × 32 × 5 × 7 = 2520

= 25 m 20 cm

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Some More Questions From Real Numbers Chapter

Express each number as a product of its prime factors: (i) 140 

Express each number as a product of its prime factors: (ii) 156 

Express each number as a product of its prime factors: (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Express each number as a product of its prime factors: (iv) 5005 

Express each number as a product of its prime factors:  (v) 7429

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.  (ii) 510 and 92 

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.  (iii) 336 and 54

Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 

Find the LCM and HCF of the following integers by applying the prime factorisation method. (ii) 17, 23 and 29