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The traffic light at three different road crossings changes after every 48 sec,72sec and 108sec respectively.If they all change simultaneously at 8:20:00 hrs,then at what time they will again change simultaneously.

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Solution : Given that traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.
48 = 2 × 2 × 2 × 2 × 3
72 = 2 × 2 × 2 × 3 × 3
108 = 2 × 2 × 3 × 3 × 3
Hence LCM of 48, 72 and 108 is (2 × 2 × 2 × 2 × 3 × 3 × 3)
 = 432
That is after 432 seconds they will change simultaneously
432 seconds = 7 min 12 seconds
Thus the traffic lights change simultaneously at 8:27:12 hrs

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