Question

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

Answer 1

Step-by-step explanation:

lcm of 48 seconds, 72 seconds and 108 seconds

= 432 sec

in minutes =432/60

7/12

that is 7minute 12sec

therefore the light will change again at 7:00+7 minutes 12 sec = 7:07:12

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