Question

the traffic lights at the three different road crossing changes after every 48 seconds 72 seconds and 108 seconds respectively.They change simultaneously at 8 am.What time will they change simultaneously again?
The options are:8.07 a.m,8.15 a.m,8.24 a.m and 8.30 a.m​

Answer 1

Answer:

Step-by-step explanation:

48 = 2⁴ x 3

72 = 2³ x 3²

108 = 2² x 3³

LCM = 2⁴ x 3³

LCM = 16 x 27 = 432

432 seconds = 432 ÷ 60 mins

432 seconds  = 7.2 mins

7.2 mins = 7 mins 12 seconds

8 am + 7 mins 12 seconds = 8.07.12 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