Traffic lights at three different crossings on a road change after every 10 minutes, 15 minutes and 20 minutes, respectively. If they change together at 9 a.m. first, when will they change together again?
Answers
Answer:
to find the at what time the lights will change simultaneously we need to find the LCM of 48, 72 and 108
Step-by-step explanation:
LCM of 42, 72 and 108
=2\times2\times3\times3\times2\times2\times3=2×2×3×3×2×2×3
432\div60\min\ =\ 7\min\ 12\ \sec432÷60min = 7min 12 sec
hence, the lights will again change simultaneously at 7mins 12sec past 7 am.
Answer:
The traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds, respectively.
So let us take the LCM of the given time that is 48 seconds, 72 seconds, 108 seconds
⇒ 48 = 2 × 2 × 2 × 2 × 3
⇒ 72 = 2 × 2 × 2 × 3 × 3
⇒ 108 = 2 × 2 × 3 × 3 × 3
Hence, LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)
LCM of 48, 72 and 108 = 432
So after 432 seconds, they will change simultaneously
We know that
60 seconds = 1 minute
so on dividing 432 / 60, we get 7 as quotient and 12 as a reminder
Hence, 432 seconds = 7 min 12 seconds
∴ The time = 7 a.m. + 7 minutes 12 seconds
Hence, the lights change simultaneously at 7:07:12 a.m