Three traffic lights change at regular intervals of 48 s, 72 s, and 108 s. If they all change simultaneously at 08:20:00, at what time will they next change together?

Introduction / Context:Simultaneous events occurring at fixed intervals repeat together every least common multiple (LCM) of those intervals. We compute the LCM in seconds and add it to the given start time to get the next simultaneous change.

Given Data / Assumptions:

• Intervals: 48 s, 72 s, 108 s
• Initial simultaneous time: 08:20:00

Concept / Approach:The next simultaneous change occurs after LCM(48, 72, 108) seconds. Convert the LCM to minutes and seconds and add to the clock time.

Step-by-Step Solution:Prime factors: 48 = 2^4 * 3; 72 = 2^3 * 3^2; 108 = 2^2 * 3^3.LCM = 2^4 * 3^3 = 16 * 27 = 432 seconds.432 s = 7 minutes 12 seconds.08:20:00 + 00:07:12 = 08:27:12.

Verification / Alternative check:Check 432 is a multiple of each interval: 432/48 = 9, 432/72 = 6, 432/108 = 4, all integers.

Why Other Options Are Wrong:Other times correspond to adding 444 s, 456 s, etc., which are not the LCM or not multiples of all three intervals.

Common Pitfalls:Mistaking gcd for LCM, or making a clock arithmetic error when adding minutes and seconds.

Final Answer:8 : 27 : 12 hrs.