7. Lighthouse Alpha and Lighthouse Bravo flash their lights every 24 seconds and 30 seconds respectively. Given that they flash together at $$ 9.15 \mathrm{p} . \mathrm{m} $$., how long will it take the lighthouses to flash their lights together again?

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1. We need to find the time interval at which both lighthouses flash together again. This is given by the least common multiple (LCM) of their flashing intervals, which are $$24$$ seconds and $$30$$ seconds.

2. First, factor each number:
   - $$24 = 2^3 \times 3$$
   - $$30 = 2 \times 3 \times 5$$

3. The LCM is found by taking the highest power of each prime that appears in any factorization:
   - For $$2$$: highest power is $$2^3$$
   - For $$3$$: highest power is $$3^1$$
   - For $$5$$: highest power is $$5^1$$

4. Therefore, 
   $$
   \text{LCM}(24, 30) = 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120 \text{ seconds}.
   $$

5. Since $$120$$ seconds is equivalent to $$2$$ minutes, the lighthouses will flash together every $$2$$ minutes.

Thus, after flashing together at $$9:15$$ p.m., they will flash together again at $$9:17$$ p.m.
The lighthouses will flash together again 2 minutes later, at 9:17 p.m.

Lighthouse Alpha and Lighthouse Bravo flash their lights every 24 seconds
and 30 seconds respectively. Given that they flash together at ., how
long will it take the lighthouses to flash their lights together again?

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Lighthouse Alpha and Lighthouse Bravo flash their lights every 24 seconds and 30 seconds respectively. Given that they flash together at ., how long will it take the lighthouses to flash their lights together again?