Question

4

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

Answer 1

Answer:

7:07:12 am

Step-by-step explanation:

we know that The traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.

So, to find in how much time they will change

simultaneously again .

We need to find LCM

48 = 2 × 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

108 = 2 × 2 × 3 × 3 × 3

hence LCM = 432 = (2 × 2 × 2 × 2 × 3 × 3 × 3)

we know 60seconds = 1 minute

so 432 seconds = 432/60 minutes = 7 minutes 12 seconds

Thus,

Required time =7am+7minutes 12seconds

=7:07:12am

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