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In a morning walk three persons step off together, their steps measure 80 cm, 85 cm, and 90 cm respectively. What is the minimum distance each should walk so that they can cover the distance in complete steps? 
  • a)
    123 m 40 cm 
  • b)
    122 m 40 cm 
  • c)
    124 m 50 cm 
  • d)
    125 m 50 cm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a morning walk three persons step off together, their steps measure...
Minimum sugar distance 
= LCM (80, 85, 90) 
= 12240 
= 122m 40 cm 
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Most Upvoted Answer
In a morning walk three persons step off together, their steps measure...
Given:
Three persons with step lengths of 80 cm, 85 cm, and 90 cm respectively.

To find:
The minimum distance each person should walk so that they can cover the distance in complete steps.

Explanation:
To find the minimum distance each person should walk, we need to find the least common multiple (LCM) of their step lengths.

Prime Factorization:
Let's write the step lengths as the product of their prime factors:
- 80 = 2^4 * 5
- 85 = 5 * 17
- 90 = 2 * 3^2 * 5

LCM:
The LCM is the product of the highest powers of all the prime factors involved:
- LCM = 2^4 * 3^2 * 5 * 17 = 13680

Distance in Complete Steps:
Now, the distance covered by each person in complete steps is the LCM of their step lengths.

Conversion:
1 meter = 100 cm
Therefore, the LCM in meters is 136.80 meters.

Answer:
The minimum distance each person should walk is 122 meters and 40 centimeters, which is option B.
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