Question

Traffic light at three different road crossing change after 48 second 72second and 108 second respectively AT what time will they change together again if they change simultaneousl at 7AM?​

Answer 1

Step-by-step explanation:

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

48 = 2 × 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

108 = 2 × 2 × 3 × 3 × 3

Taking LCM for,

48, 72 and 108 i.e (2 × 2 × 2 × 2 × 3 × 3 × 3)= 432

We have,

432 seconds = 7 min 12 seconds

Find the time it will change together again:

8 am + 7 mins 12 seconds = 8.07.12 am

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