Question

the traffic lights at three different road crossings change after every 48 seconds 72 seconds and 108 seconds respectively if the changes simultaneously at 7 a.m. at what time will be the change simultaneously again​

Answer 1

Step-by-step explanation:

first simultaneously at 7:00am

change =7:00am +48seconds

=7hours 48 sec (first crossing)

first simultaneously at 7:00am

change=7:00am+72 seconds

=7 hours+1 minute 12 seconds

=7 hours 1 minute 12 seconds (2nd crossing)

first simultaneously at 7:00am

change=7:00am +108 sec

=7 hours+1minute 48seconds

=7 hours 1 minute 48seconds(3rd crossing)

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