UPSC Prelims 2011·CSAT·Quantitative Aptitude·Number System

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?

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Last updated 23 May 2026, 3:31 pm IST
  1. A25 m 20 cmCorrect
  2. B50 m 40 cm
  3. C75 m 60 cm
  4. D100 m 80 cm

Explanation

This problem requires finding the Least Common Multiple (LCM) of the given step lengths to determine the minimum distance each person can cover in complete steps. 1. Identify the step lengths: 40 cm, 42 cm, and 45 cm. 2. Calculate the LCM of 40, 42, and 45. Prime factorization: 40 = 2^3 * 5 42 = 2 * 3 * 7 45 = 3^2 * 5 LCM = 2^3 * 3^2 * 5 * 7 = 8 * 9 * 5 * 7 = 72 * 35 = 2520 cm. 3. Convert the LCM from centimeters to meters and centimeters: Since 100 cm = 1 m, 2520 cm = 2500 cm + 20 cm = 25 m 20 cm. Therefore, the minimum distance each should walk is 25 m 20 cm. Analyzing the options: A) 25 m 20 cm - This matches our calculated LCM. B) 50 m 40 cm - This is 2 * 25 m 20 cm, which is a multiple but not the minimum. C) 75 m 60 cm - This is 3 * 25 m 20 cm, which is a multiple but not the minimum. D) 100 m 80 cm - This is 4 * 25 m 20 cm, which is a multiple but not the minimum. The final answer is A.
Quantitative Aptitude: Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum di
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