At Frantic Junction, trains arrive at regular intervals on three different lines. On the line from Aytown, trains arrive every $$15$$ minutes. On the line from Beeville, they arrive every $$12$$ minutes and from Ceeford they arrive every $$8$$ minutes. At $$10:00\text{ am}$$ a train from each town arrives at Frantic Junction. What is the next time that three trains will arrive together. 
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