Question

the traffic lights at three diffrent road crossing change after every 36 seconds ,48 seconds and 72 seconds respectively .If they change simultaneously at 8:30 am at what time will they change simultaneously again​

Answer 1

Answer:

here is your answer,

36=2 × 2 × 3 × 3

48=2 × 2 × 2 × 2 × 3

72=2 × 2 × 2 × 3 × 3

Taking LCM,

36, 48 and 72 i.e (2× 2 × 2 × 2 × 3 × 3) = 144

We have,

144 seconds = 2 min 4 seconds

Hence, after 2 min and 4 seconds they will change simultaneously.

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Answer 2

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If the traffic lights change simultaneously at 8 :30 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 + 37 minutes 12 seconds

08 : 37 : 12 am