Answer:
8:07:12 am
Explanation:
The lights will change simultaneously after any multiple of the least common multiple of their cycle times.
LCM
The least common multiple of a set of numbers is the product of the highest powers of their prime factors.
48 = 2⁴×3
72 = 2³×3²
108 = 2²×3³
The highest power of the factor 2 is 4. The highest power of the factor 3 is 3, so the LCM of the numbers 48, 72, and 108 is ...
LCM = 2⁴×3³ = 16×27 = 432
The lights will change simultaneously after each period of 7 minutes 12 seconds. They will change simultaneously again at 8:07:12 am.