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Bus departures from depot

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$2$ bus lines leave a depot together at time $0$ . Line A departs every $12$ minutes and line B every $18$ minutes. After how many minutes do they next depart at the same moment?

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Hint

Look for the smallest common multiple of the $2$ intervals.

Solution

The buses depart together again at the least common multiple of $12$ and $18$ .
Factor: $12 = 2^{2} \times 3$ and $18 = 2 \times 3^{2}$ .
Take the highest powers: $2^{2} \times 3^{2} = 36$ .
The answer is $36$ .

Answer: $36$

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