Question

Three athletes A, B, C are participating in a racing event. They start running together. A takes 30 seconds to complete one round on the track, B takes 40 seconds and C takes 45 seconds. What is the minimum number of seconds after which will they all be at the same place again?

• A. 180 seconds
• B. 240 seconds
• C. 360 seconds
• D. 720 seconds

Answer 1

The correct option is C

360 seconds

The athletes will be at the same place after the time which is the LCM of the times required to complete one round for each athlete.
Therefore, minimum number of seconds after which they all will be at the same place again = LCM (30, 40, 45)

$\begin{array}{cc}5& 30,40,45\\ 3& 6,8,9\\ 3& 2,8,3\\ 2& 2,8,1\\ 2& 1,4,1\\ 2& 1,2,1\\ & 1,1,1\end{array}$

LCM (30, 40, 45)

= $5\times 3\times 3\times 2\times 2\times 2$

= 360 seconds