Question

Two radio stations are playing this week's #1 hit song. One radio station

plays the song every 18 minutes. The other radio station plays the song
every 24 minutes. Both stations play the song at 3:00 PM. When is the
next time the stations will play the song at the same time? Explain

Answer 1

The next time the two radio stations will play the song at the same time is 72 minutes after they started playing at 3:00 PM; at 4:12 PM.

Step-by-step explanation:

To find the next time the two radio stations will play the song at the same time, we need to find the least common multiple (LCM) of 18 minutes and 24 minutes. The LCM is the smallest number that is divisible by both 18 and 24.

Prime factorizing the numbers, we have:
18 = 2 * 3 * 3
24 = 2 * 2 * 2 * 3

Now, we take the highest power of each prime factor:
2^3 * 3^2 = 72

Therefore, the two radio stations will play the song at the same time again after 72 minutes. Since they started playing at 3:00 PM, the next time they will play the song together is at 4:12 PM.

Answer 2

The next time the stations will play the song at the same time is 4:12.

Step-by-step explanation:

To answer this question, we need to find the number of minutes where the stations overlap. Station 1 plays the song every 18 minutes, while station 2 does it every 24 minutes. Let's start multiplying the minutes to see where they overlap.

18 x 1 = 18 24 x 1 = 24

18 x 2 = 36 24 x 2 = 48

18 x 3 = 54 24 x 3 = 72

18 x 4 = 72

According to the information above, both stations will be playing the song 72 minutes after 3:00, which means 4:12. Notice that station 1 will have played it 4 times, while station 2, only 3.