In a fire range, 4 shooters are firing at their respective targets. The first, the second, the third and the fourth shooter hit the target once in every 5s, 6s,7s and 8s,respectively.If all of them hit their targets at 9:00 am, when will they hit their targets together again?

Options

A. `9:04 AM`
B. `9:08 AM`
C. `9:14 AM`
D. None of the above

Answer

To solve the problem of when all four shooters will hit their targets together again, we need to find the least common multiple (LCM) of the time intervals at which they hit their targets. The shooters hit their targets every 5 seconds, 6 seconds, 7 seconds, and 8 seconds respectively.

### Step-by-Step Solution:

1. **Identify the time intervals**:
- Shooter 1: 5 seconds
- Shooter 2: 6 seconds
- Shooter 3: 7 seconds
- Shooter 4: 8 seconds

2. **Find the LCM of the time intervals**:
- To find the LCM, we can use the prime factorization method.
- Prime factorization of each number:
- 5 = 5^1
- 6 = 2^1 × 3^1
- 7 = 7^1
- 8 = 2^3

3. **Take the highest power of each prime factor**:
- From the factorizations, we take:
- 2^3 (from 8)
- 3^1 (from 6)
- 5^1 (from 5)
- 7^1 (from 7)

4. **Calculate the LCM**:
- LCM = 2^3 × 3^1 × 5^1 × 7^1
- LCM = 8 × 3 × 5 × 7
- First, calculate 8 × 3 = 24
- Then, 24 × 5 = 120
- Finally, 120 × 7 = 840

5. **Convert seconds to minutes**:
- Since 840 seconds is the time until they all hit their targets together again, we convert this into minutes.
- 840 seconds ÷ 60 seconds/minute = 14 minutes

6. **Determine the time they will hit together again**:
- They all hit their targets together at 9:00 AM.
- Adding 14 minutes to 9:00 AM gives us 9:14 AM.

### Final Answer:
They will all hit their targets together again at **9:14 AM**.

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