The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

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Solution

Time period after which these lights will change = LCM of 48, 72, 108

2

48, 72, 108

2

24, 36, 54

2

12, 18, 27

2

6, 9, 27

3

3, 9, 27

3

1, 3, 9

3

1, 1, 3

1, 1, 1

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432

They will change together after every 432 seconds i.e., 7 min 12 seconds.

Hence, they will change simultaneously at 7:07:12 am.

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2	48, 72, 108
2	24, 36, 54
2	12, 18, 27
2	6, 9, 27
3	3, 9, 27
3	1, 3, 9
3	1, 1, 3
	1, 1, 1