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: On a morning walk, three persons step out together and their steps measure 30 cm, 36 cm and 40 cm respectively. What is the minimum distance each should walk so that each can cover the same 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

30 = 2 × 3 × 5

36 = 2² × 3²

40 = 2³ × 5

Step 3: Find the LCM

LCM = 2³ × 3² × 5

LCM = 8 × 9 × 5

LCM = 360 cm

Step 4: Convert into Metres (Optional)

360 cm = 3.6 m

Final Answer

∴ The minimum distance each person should walk so that all can cover it in complete steps is 360 cm or 3.6 metres.

Conclusion

Thus, by finding the LCM of the step lengths 30 cm, 36 cm and 40 cm, we get the minimum distance required as 360 cm.