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

Answer 1

The Correct Option is A

To find the minimum distance each person should walk so that they all cover the same distance in complete steps, we need to determine the Least Common Multiple (LCM) of their step measurements. The step measurements are 40 cm, 42 cm, and 45 cm.

Step 1: Find the prime factors of each number:

• 40 = 2³ × 5
• 42 = 2 × 3 × 7
• 45 = 3² × 5

Step 2: Determine the LCM by taking the highest power of all prime factors present:

LCM = 2³ × 3² × 5 × 7

Step 3: Calculate the LCM:

• 2³ = 8
• 3² = 9

So, LCM = 8 × 9 × 5 × 7 = 2520 cm

Step 4: Convert the LCM from centimeters to meters:

2520 cm = 2520 ÷ 100 = 25.20 meters

Thus, the minimum distance each person should walk so that they all cover the same distance in complete steps is 25 meters and 20 centimeters, which matches the option "25 m 20 cm".