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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.

Solution

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

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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

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