Question

Traffic lights at three different road crossing change after 48 seconds, 72 seconds
and 108 seconds respectively. At what time will they change together again if they
change simultaneously at 7 A.M.?​

Answer 1

Answer:

2 P.M.

Step-by-step explanation:

The LCM of 48,72,108= 432

When it is divided by 60then the quotient is 7 and remainder is 12.

7A.M.+7=14=2P.M. and 12 sec

Answer 2

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If the traffic lights change simultaneously at 7 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:

7 am + 7 minutes 12 seconds

07 : 07 : 12 am