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

Here is a second way, using the division ladder method instead of writing out full prime factorisations.

1. Set up the ladder. Write 40, 42, 45 in a row and repeatedly divide by any prime that divides at least one of them, carrying down the numbers that are not divisible unchanged.
2. Divide by 2 twice. $40,42,45 \to 20,21,45 \to 10,21,45$ (only 20 was still even on the second pass).
3. Divide by 3. $10,21,45 \to 10,7,15$.
4. Divide by 5. $10,7,15 \to 2,7,3$.
5. No common factor remains among 2, 7, 3, so stop. Multiply every divisor used ($2,2,3,5$) by the final row ($2,7,3$): $\text{LCM}=2\times2\times3\times5\times2\times7\times3=2520$.
6. Convert to metres. $2520$ cm $=25$ m $20$ cm.

This ladder approach gives the same LCM as prime factorisation, confirming option A. \[ \boxed{25\ \text{m}\ 20\ \text{cm}} \]