On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each cancover the same distance in complete steps
Solution:
The LCM of 40 cm, 42 cm and 45 cm has to be found to get the required minimum distance.
Now,
40 = 2 × 2 × 2 × 5
42 = 2 × 3 × 7
45 = 3 × 3 × 5
LCM(40, 42, 45) = 2 × 3 × 5 × 2 × 2 × 3 × 7
= 2520.
Therefore, the minimum distance each should walk is 2520 cm so that each can cover the same distance in complete steps.
✦ Try This: On a morning walk, three persons step off together and their steps measure 80 cm, 85 cm and 90 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps
We have to find the LCM of 80 cm, 85 cm and 90 cm to get the required minimum distance.
For this,
80 = 2 × 2 × 2 × 2 × 5
85 = 17 × 5
90 = 2 × 3 × 3 × 5
LCM(80, 85, 90)
= 2 × 2 × 3 × 5 × 2 × 2 × 3 × 17
= 12240
Therefore, the minimum distance each should walk is 12240 cm so that each can cover the same distance in complete steps.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1
NCERT Exemplar Class 10 Maths Exercise 1.3 Problem 12
On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps
Summary:
The minimum distance each should walk is 2520 cm so that each can cover the same distance in complete steps.
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