Bus A departs Tampines MRT every 6 minutes. Bus B departs the same stop every 9 minutes. Bus C departs the same stop every 4 minutes. All three buses depart together at 8:00 a.m. What is the EARLIEST time after 8:00 a.m. when all three buses depart at the same time again?
Show Worked Solution
Worked Solution
Step 1: To find when all three buses next depart together, find the LCM of 6, 9 and 4.
Step 2: Find LCM(6, 9) first. List multiples of 9: 9, 18, 27, ... List multiples of 6: 6, 12, 18, ... The first common multiple is 18. So LCM(6, 9) = 18.
Step 3: Now find LCM(18, 4). List multiples of 18: 18, 36, 54, ... List multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, ... The first common multiple is 36. So LCM(18, 4) = 36.
Step 4: Add 36 minutes to 8:00 a.m. 8:00 a.m. + 36 minutes = 8:36 a.m.
Answer: The earliest time is 8:36 a.m.
Correct answer: 8:36 a.m.
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