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The traffic lights at three different road crossings change after every 48, 72 and 108 seconds respectively. If they change simultaneously at 8 am, at what time will they change to again?​

Sagot :

sqdancefan

Answer:

  8:07:12 am

Step-by-step explanation:

The lights will change simultaneously after any multiple of the least common multiple of their cycle times.

LCM

The least common multiple of a set of numbers is the product of the highest powers of their prime factors.

  48 = 2⁴×3

  72 = 2³×3²

  108 = 2²×3³

The highest power of the factor 2 is 4. The highest power of the factor 3 is 3, so the LCM of the numbers 48, 72, and 108 is ...

  LCM = 2⁴×3³ = 16×27 = 432

The lights will change simultaneously after each period of 7 minutes 12 seconds. They will change simultaneously again at 8:07:12 am.

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