Three girls start jogging from the same point around a circular track and each one completes one round in 24 seconds, 36 seconds and 48 seconds respectively. After how much time will they meet at one point?

### Concept & Strategy When objects move around a closed circular track starting from the same point, they will meet again at the starting point after a time equal to the Least Common Multiple (LCM) of the times taken by each to complete one full revolution. $$\text{Meeting Time} = \text{LCM}(T_1, T_2, T_3)$$ ### Step-by-Step Solution **Given:** * Revolution time for Girl 1 = 24 seconds * Revolution time for Girl 2 = 36 seconds * Revolution time for Girl 3 = 48 seconds **Calculation:** 1. Find the LCM of 24, 36, and 48: * Prime factorization: * $24 = 2^3 \times 3$ * $36 = 2^2 \times 3^2$ * $48 = 2^4 \times 3$ * Take the highest powers of all prime factors present: * $\text{LCM} = 2^4 \times 3^2 = 16 \times 9 = 144 \text{ seconds}$ 2. Convert the result into minutes and seconds to match the options: * $\frac{144}{60} = 2 \text{ with a remainder of } 24$ * Time = 2 minutes and 24 seconds ### Exam Strategy & Shortcut You can spot the LCM much faster by looking at the largest number (48) and testing its multiples against the other numbers: * $48 \times 1 = 48$ (Not divisible by 36) * $48 \times 2 = 96$ (Not divisible by 36) * $48 \times 3 = 144$ (Divisible by 24 and 36) Thus, 144 is the LCM. 144 seconds is exactly 2 minutes and 24 seconds. ### Common Pitfall A common mistake in cyclical track problems is confusing "meeting at the starting point" with "meeting anywhere on the track." The LCM specifically gives the time for meeting *at the starting point*. In this specific question phrasing, "meet at one point" implies the starting point constraint as defined by standard aptitude conventions. ### Final Answer **Therefore, the correct answer is 2 minutes 24 seconds.**