Three lighthouses flash their lights at intervals of 6 seconds, 9 seconds and 15 seconds respectively. They all flash together at 8:00 a.m. At what time will they next flash all together?
Show Worked Solution
Worked Solution
Step 1: To find when all three flash together again, compute the LCM of 6, 9 and 15.
Step 2: Prime factorise each interval.
6 = 2 × 3, 9 = 3 × 3, 15 = 3 × 5.
Step 3: Take the highest power of each prime that appears.
LCM = 2 × 3² × 5 = 2 × 9 × 5 = 90 seconds.
Step 4: Convert 90 seconds to minutes and seconds.
90 s = 1 minute 30 seconds.
Step 5: Add to 8:00 a.m. to find the next coincidence.
Next time = 8:00 a.m. + 1 min 30 s = 8:01:30 a.m.
Answer: 8:01:30 a.m.
Correct answer: 8:01:30 a.m.
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