Question

Three persons start walking 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?

• A. 25 m 20 cm
• B. 50 m 40 cm
• C. 75 m 60 cm
• D. 100 m 80 cm

Hint:

The answer is simply the LCM of 40, 42, and 45 converted to metres and centimetres.

Answer 1

The Correct Option is A

Step 1: Understand what "minimum distance in complete steps" means.
Each person covers distance in whole numbers of their own steps. For all three to finish at exactly the same point after a whole number of steps each, the distance walked must be a common multiple of 40 cm, 42 cm, and 45 cm. The minimum such distance is the LCM of these three numbers.

Step 2: Find the prime factorisation of each step length.
\(40=2^3\times5\)
\(42=2\times3\times7\)
\(45=3^2\times5\)

Step 3: Take the highest power of each prime and multiply.
\[ \text{LCM} = 2^3\times3^2\times5\times7 = 8\times9\times5\times7 = 2520\text{ cm} \]

Step 4: Convert to metres and centimetres.
\(2520\) cm \(= 2500\) cm \(+20\) cm \(= 25\) m \(20\) cm.

Final Answer:
The minimum distance each person should walk is 25 m 20 cm, so option A is correct. \[ \boxed{25\ \text{m}\ 20\ \text{cm}} \]