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Question
The traffic lights at three different road junctions change after every 40 seconds, 60 seconds and 72 seconds respectively. If they changed simultaneously together at 8 a.m at the junctions, at what time will they simultaneously change together again?
Solution
This is an LCM related problem
Finding the LCM of 40, 60 and 72
60 seconds = 1 min
360 min = 6 min
| 2 | 40, 60, 72 |
| 2 | 20, 30, 36 |
| 3 | 10, 15, 18 |
| 5 | 10, 5, 6 |
| 2 | 2, 1, 6 |
| 3 | 1, 1, 3 |
| 1, 1, 1 |
LCM (40, 60, 72) = 2 × 2 × 3 × 5 × 2 × 3 = 360
After 360 seconds they will change again i.e after six minutes they will change again i.e at 8.06 am they will change again simultaneously.
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