Minimum Distance to Be Walked in Complete Steps by Three Persons

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: In a morning walk, three persons step off together, their steps measuring 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that he can cover the distance in complete steps?

Step 1: Identify the Mathematical Concept

The minimum distance that can be covered in complete steps by all three persons is the LCM (Least Common Multiple) of their step lengths.

Step 2: Prime Factorisation of the Step Lengths

80 = 2⁴ × 5

85 = 5 × 17

90 = 2 × 3² × 5

Step 3: Find the LCM

LCM = 2⁴ × 3² × 5 × 17

LCM = 16 × 9 × 5 × 17

LCM = 12240 cm

Step 4: Convert into Metres (Optional)

12240 cm = 122.4 m

Final Answer

∴ The minimum distance each person should walk so that all can cover it in complete steps is 12240 cm or 122.4 metres.

Conclusion

Thus, by finding the LCM of the step lengths 80 cm, 85 cm and 90 cm, we get the minimum distance required as 12240 cm.