Question

the traffic lights at three different road Crossings change after every 48 seconds 72 seconds and 108 seconds respectively if they change simulants Li at 8 a.m. at what time will the change simultaneously again​

Answer 1

Answer:

8.07.12 am

Step-by-step explanation:

Find the Prime Factors:

48 = 2⁴ x 3

72 = 2³ x 3²

108 = 2² x 3³

Find the LCM:

LCM = 2⁴ x 3³

LCM = 16 x 27 = 432

Convert 432 seconds to mins:

432 seconds = 432 ÷ 60 mins

432 seconds = 7.2 mins

7.2 mins = 7 mins 12 seconds

Find the time it will change together again:

8 am + 7 mins 12 seconds = 8.07.12 am

Answer: It will change together again at 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