Question

The traffic lights at three different road functions change after every 40 seconds,

60 seconds and 72 seconds respectively. If they changed simultaneously together at

8 a.m at the functions, at what time will they simultaneously change together again"​

Answer 1

Answer:

Lights will change simultaneously together at 8:06 A.M

Step-by-step explanation:

Given that-

The traffic lights change after every 40 seconds, 60 seconds and 72 seconds.

Finding L.C.M of 40, 60 and 72

40 = 2×2×2×5

60 = 2×2×3×5

72 = 2×2×2×3×3

L.C.M. = 2×2×2×3×3×5

L.C.M. = 360 seconds

We know that-

60 seconds = 1 minute

1 seconds = $\dfrac{1}{60}minutes$

360 seconds = $\dfrac{1*360}{60} minutes$

360 seconds = 6 minutes

Since the lights changed simultaneously together at 8 A.M

Then they will change next time = 8 A.M. + 6 minute

Therefore lights will change simultaneously together at 8:06 A.M

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. 40 s, 72 s and 60 s.

LCM of these durations by prime factorisation

• 40 = 2 × 2 × 2 × 5 = 2³ × 5
• 60 = 2 × 2 × 3 × 5
• 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

LCM of 40, 72 and 60 is 2³ × 3² × 5 = 360 seconds.

Hence, They will change after 360 seconds i.e. 6 minutes.

The traffic lights will change after:

• 8 am + 6 minutes
• 08 : 06 am