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Problem #83 · October 18, 2026

EKUB — greatest common divisor and EKUK — least common multiple

From the stop, a bus on the first route departs every 12 minutes, and a bus on the second route departs every 18 minutes. At 9:00 both buses departed together. At what time will they next depart together again?
  1. A9:06
  2. B9:30
  3. C9:36
  4. D9:54
  5. E10:12

WORKED EXAMPLE

Solution

The period at which both buses depart together equals EKUK(12;18)EKUK(12; 18). 12=22⋅312 = 2^2 \cdot 3, 18=2⋅3218 = 2 \cdot 3^2, so EKUK=22⋅32=36EKUK = 2^2 \cdot 3^2 = 36 minutes. Therefore the next joint departure is from 9:00 after 36 minutes have passed, that is, at 9:36.
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