Question

the traffic light at three different road crossing changes after every 24 seconds, 36 seconds,and 54 seconds respectively. if they change simultaneously at 10:00 a.m at what time they change simultaneously again?​

Answer 1

Answer:

10:03:36

Step-by-step explanation:

after 216 seconds use LCM you will get 3 twos and 3 threes 3*3*3*2*2*2=216

216 seconds is 03:36

Answer 2

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If the traffic lights change simultaneously at 10 a.m, then they will change simultaneously again after the LCM of the duration i.e. 24 s, 36 s and 54 s.

LCM of these durations by prime factorisation

• 24 = 2 × 2 × 2 × 3 = 2³ × 3
• 36 = 2 × 2 × 3 × 3 = 2² × 3²
• 54 = 2 × 3 × 3 × 3 = 2 × 3³

LCM of 48, 72 and 108 is 2³ × 3³ = 216 seconds.

Hence, They will change after 216 seconds i.e. 3 minutes 36 seconds.

The traffic lights will change after:

• 10 am + 3 minutes 36 seconds
• 10 : 03 : 36 am