Using the least common factor, it is found that it will take 120 days until all four buses return to the terminal on the same day.
- Considering their itineraries, the number of days it will take until all four buses return to the terminal on the same day is the lcm of 6, 8, 10 and 15.
To find their least common factor, we factor each number by prime numbers, hence:
6 - 8 - 10 - 15|2
3 - 4 - 5 - 15|2
3 - 2 - 5 - 15|2
3 - 1 - 5 - 15|3
1 - 1 - 5 - 5|5
1 - 1 - 1 - 1
Hence, lcm(6, 8, 10, 15) = 2³ x 3 x 5 = 8 x 15 = 120.
It will take 120 days until all four buses return to the terminal on the same day.
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