Question

the traffic lights at three different road crossings change after every 48 seconds 72 seconds and108 secs .if they all change simultaneously at 8hours then, at what time will be again change simultaneously .​

Answer 1

Answer:

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Step-by-step explanation:

FIRST WE HAVE TO FIND THE LCM OF 48, 72 AND 108 WHICH IS 432 SECS .

AFTER THAT CONVERT SECS INTO MINS :- 432/60 = 7.2 = 7.12 MIN

IN THE QUESTION IT IS GIVEN THAT they all change simuntaneously at 8 hours

SO THE REQUIRED TIME IS AT 8:7:12

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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