Math CentralQuandaries & Queries


Question from Stephanie, a parent:

Starting at 8:00a.m., a passenger plane leaves from an airport every 6 minutes and a cargo plane leaves every 7 minutes. When is the next time these kinds of planes will leave at the same time?

Hi Stephanie,

Suppose you keep track of the number of minutes after 8:00 am when the trains leave. The first train leaves at

\[6, 2\times6, 3\times 6, \cdot, \cdot, \cdot \mbox{ and so on.}\]

The second train leaves at

\[7, 2\times7, 3\times 7, \cdot, \cdot, \cdot \mbox{ and so on.}\]

What is the first number tat appears in both lists? What time is that?


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