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.