One radio station broadcasts a weather forecast every 18 minutes and another station broadcasts a commercial every 15 minutes. if the stations broadcasts both a weather forecast and a commercial at noon, when is the next time that both will be broadcasted at the same time.

The correct answer is:

1:30 PM.

Explanation:

To do this, we first find the LCM (least common multiple) of the two numbers.  We do this by finding the prime factorization of each:

18 = 9×2

9 = 3×3

So 18 = 2×3×3.

15 = 3×5

For the LCM, we start with the GCF (greatest common factor).  The only common factor is 3.  Next we take the uncommon factors; these are 2, 3 and 5.  This makes our LCM

3(2×3×5) = 3(30) = 90

This means both will air every 90 minutes.  90 minutes is an hour and a half; an hour and a half past noon is 1:30 PM.

a

step-by-step explanation:

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