Question

The traffic lights at three different road – crossing change after every 36 seconds,
60 seconds and 72 seconds. If they change simultaneously at 8 a. m. after, what
time will they change again simultaneously?

Answer 1

Answer:

8:06am

Step-by-step explanation:

36 => 2^2 × 3^2

60 => 2^2 × 3 × 5

72 => 2^3 × 3^2

therefore,

LCM = 2^3 × 3^2 × 5

=8 × 9 × 5

= 72 ×5

= 360 seconds

therefore,

360 seconds = 360/60 = 6 minutes

So, after 8:00 they will change at 8:06 simultaneously

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

36 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

60 = 5 × 3 × 2²

72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

LCM of 48, 72 and 108 is 2⁴ × 3³ = 360 seconds.

Hence, They will change after 360 seconds i.e. 6 minutes 12 seconds.

The traffic lights will change after:

8 am + 6 minutes

08 : 06 : 00 am