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Problem #86 · October 21, 2026

EKUB — greatest common divisor and EKUK — least common multiple

Three lights each flash once every 6, 8 and 12 seconds, respectively. Right now all three flashed together. After how many seconds will they flash together again for the first time?
  1. A2
  2. B24
  3. C26
  4. D48
  5. E576

WORKED EXAMPLE

Solution

The period at which all three lights flash together equals EKUK(6;8;12)EKUK(6; 8; 12). Because 6=2⋅36 = 2 \cdot 3, 8=238 = 2^3, 12=22⋅312 = 2^2 \cdot 3, we have EKUK=23⋅3=24EKUK = 2^3 \cdot 3 = 24. Therefore they flash together every 24 seconds.
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