On a road, three consecutive traffic lights change after 36, 42 and 72

We are given that three consecutive traffic lights change after 36, 42, and 72 seconds, respectively. To determine at what time they will change simultaneously, we need to determine the least common multiple of 36, 42, and 72. Let’s first break each number into prime factors:

36 = 9 x 4 = 3^2 x 2^2

42 = 6 x 7 = 2^1 x 3^1 x 7^1

72 = 9 x 8 = 3^2 x 2^3

To determine the LCM, we multiply the unique prime factors along with their respective largest exponent.

Thus, the LCM of 36, 42, and 72 = 2^3 x 3^2 x 7^1 = 504.

Let’s now convert 504 seconds into minutes and seconds.

504 seconds = 504/60 minutes = 8 24/60 minutes = 8 minutes and 24 seconds.

Since the lights started at 9 a.m., they will simultaneously change at 9:08:24.

Answer: B

504 sec
8 min 24 sec

Posted from my mobile device

Take the lcm and convert seconds to minutes

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