Answer :
Final answer:
The lights on the lighthouse will next flash together in 280 seconds or 4 minutes and 40 seconds.
Explanation:
Let's find the least common multiple (LCM) of 14 seconds and 2 minutes, which is the time it takes for the lights to flash together again. The prime factorization of 14 is 2 * 7 and the prime factorization of 2 minutes is 2 * 2 * 2 * 5. To find the LCM, we take the highest power of each prime factor: 2 * 2 * 2 * 5 * 7 = 280. Therefore, the lights will next flash together in 280 seconds or 4 minutes and 40 seconds.
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