Question

The traffic lights at three different road crossing change after 24 seconds, 30 seconds and 36 seconds respectively. If they change simultaneously at 8:00 a.m.,at what time will they change simultaneously again ?

Answer 1

LCM of 24 = 2^3 * 3

LCM of 30 = 2 * 3 * 5

LCM of 36 = 2^2 * 3^2

LCM of 24,30,36 = 2^3 * 3^2 * 5

                             = 360

After 360 seconds they will change simultaneously.

They will change simultaneously again at 8:06:00 am.

Answer 2

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If the traffic lights change simultaneously at 8 a.m, then they will change simultaneously again after the LCM of the duration i.e. 48 s, 72 s and 108 s.

LCM of these durations by prime factorisation

48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³

LCM of 48, 72 and 108 is 2⁴ × 3³ = 432 seconds.

Hence, They will change after 432 seconds i.e. 7 minutes 12 seconds.

The traffic lights will change after:

8 am + 7 minutes 12 seconds

08 : 07 : 12 am