To determine when Priya and Ravish will meet again at the starting point after they begin their laps around the circular path, we need to find the least common multiple (LCM) of the time it takes each of them to complete one round. Priya takes 18 minutes, and Ravish takes 12 minutes. The LCM will give us the first time after they start that both will be back at the starting point simultaneously.
Finding the LCM
The least common multiple of two numbers is the smallest number that is a multiple of both. To find the LCM of 18 and 12, we can use the prime factorization method:
Step 1: Prime Factorization
- 18 can be factored into primes as: 2 × 3²
- 12 can be factored into primes as: 2² × 3
Step 2: Identify the Highest Powers
Next, we take the highest power of each prime number that appears in the factorizations:
- For the prime number 2, the highest power is 2² (from 12).
- For the prime number 3, the highest power is 3² (from 18).
Step 3: Calculate the LCM
Now, we multiply these highest powers together to find the LCM:
LCM = 2² × 3² = 4 × 9 = 36
Conclusion
This means that Priya and Ravish will both be back at the starting point together after 36 minutes. To summarize:
- Priya completes a round in 18 minutes.
- Ravish completes a round in 12 minutes.
- They will meet again at the starting point after 36 minutes.
So, the answer to your question is that they will meet again at the starting point after 36 minutes. This approach not only helps in solving this problem but also reinforces the concept of LCM, which is useful in various real-life situations involving cycles and periodic events.
