Three friends Rudra, Siva and Anvesh start running together from the same point around a circular stadium track. They take 24 seconds, 36 seconds and 30 seconds respectively to complete one full revolution of the track. After how many minutes will all three friends be together again at the starting point for the first time?

Introduction / Context:
This question tests knowledge of least common multiple in the context of circular motion and repeating events. Each friend completes one lap in a different fixed time. We are asked when they will all be back together at the starting point at the same instant for the first time after starting.

Given Data / Assumptions:

• Rudra completes one revolution in 24 seconds.
• Siva completes one revolution in 36 seconds.
• Anvesh completes one revolution in 30 seconds.
• They all start together from the same point at the same time.
• We must find the first time when all three are again simultaneously at the starting point, expressed in minutes.

Concept / Approach:
Each runner returns to the starting point at integer multiples of his own lap time. Therefore, the first time when all three are together at the start again is when the time elapsed is a common multiple of 24, 36 and 30 seconds. The smallest such time is the least common multiple (LCM) of these three numbers. We find the LCM in seconds and then convert it to minutes.

Step-by-Step Solution:
We need LCM(24, 36, 30). Prime factorisation: 24 = 2^3 * 3, 36 = 2^2 * 3^2, 30 = 2 * 3 * 5. For the LCM, take the highest power of each prime: 2^3, 3^2 and 5. Compute LCM = 2^3 * 3^2 * 5 = 8 * 9 * 5 = 72 * 5 = 360 seconds. Convert 360 seconds to minutes: 360 / 60 = 6 minutes. Therefore, they will meet at the starting point again after 6 minutes.

Verification / Alternative check:
After 6 minutes, or 360 seconds, the number of laps for each friend is an integer: Rudra runs 360 / 24 = 15 laps, Siva runs 360 / 36 = 10 laps and Anvesh runs 360 / 30 = 12 laps. Since each has completed an integer number of full revolutions, all three are back at the starting point together at 6 minutes.

Why Other Options Are Wrong:
Options like 60 or 120 minutes are larger common multiples but not the least one, so they do not give the earliest meeting time. The value 360 minutes misinterprets the LCM as minutes instead of seconds. Three minutes is not a common multiple of 24, 36 and 30 seconds, so they would not all be back at the start at that time.

Common Pitfalls:
Learners sometimes confuse LCM with greatest common divisor or forget to convert the final answer into the requested units. Another frequent error is to work with approximate multiples instead of exact prime factorisation, which can lead to missing the true least common multiple.

Final Answer:
They will all meet at the starting point again after 6 minutes.