Question

A, B and C start to run round a circular stadium at the same time, in the same direction. A completes a round in 252 seconds, B completes in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?

Answer 1

Hint: The above question is based on the concept of least common multiple. The main approach towards solving this is to calculate the least common multiple of the given completed time of A, B, C because at what sooner time all three of them reach a common time at the starting point.

Complete step-by-step solution:
In mathematics the least common multiple of two or more numbers is the smallest number which is the multiple of all the numbers.
In the above given question, A,B and C start running around a circular stadium and all of them are running in the same direction.
So now we need to find out what common time will all three of them meet again at the starting point. So individual time are given as follows:
A completes in 252 seconds, B completes in 308 seconds and C completes 198 seconds.
So by calculating the LCM of all the three numbers
$
  252 = 2 \times 2 \times 3 \times 3 \times 7 \\
  308 = 2 \times 2 \times 7 \times 11 \\
  198 = 2 \times 3 \times 3 \times 11 \\
    \\
 $
So the required LCM is
\[2 \times 2 \times 3 \times 3 \times 7 \times 11 = 2772\]

Hence, we get 2772 seconds which is the correct answer.

Note: An important thing to note is that we get the answer in seconds which is the common time at which A,B and C will meet .We can also convert this into minutes and seconds by dividing it by 60,we get quotient as 46 and remainder as 12.Therefore we get 46min 12 sec.