7. Uighthouse Alpha and Lighthouse Eravo flash their lights every 24 seconds and 30 seconds respectiveli. Given that they flash together at 9.15 pm., hot long will it fake the lighthouses to flash their lights together again?

1. We first determine the flashing frequencies: - Lighthouse Alpha flashes every \(24\) seconds. - Lighthouse Eravo flashes every \(30\) seconds. 2. To find when they flash together again, we need to find the least common multiple (LCM) of \(24\) and \(30\). 3. Factorize both numbers: - \(24 = 2^3 \times 3\) - \(30 = 2 \times 3 \times 5\) 4. The LCM is found by taking the highest power of each prime factor: \[ \text{LCM}(24, 30) = 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120 \] 5. Hence, the lighthouses will flash together every \(120\) seconds. 6. Convert seconds to minutes: \[ 120 \text{ seconds} = \frac{120}{60} = 2 \text{ minutes} \] 7. Since they flash together at \(9:15\) pm, they will next flash together at: \[ 9:15 \text{ pm} + 2 \text{ minutes} = 9:17 \text{ pm} \]