Question

1

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 3pm. How many minutes will pass before they play the same song again.

Answer 1

Answer: 72 minutes

======================================================

Step-by-step explanation:

The GCF of 18 and 24 is 6, since this is the largest factor shared between the two numbers

• 18 = 6*3
• 24 = 6*4

To find the LCM, we'll involve the GCF. The LCM of two numbers x and y is found by multiplying them, and then dividing over the GCF of them.

LCM of x and y = (x*y)/(GCF of x and y)

LCM of 18 and 24 = (18*24)/6

LCM of 18 and 24 = 432/6

LCM of 18 and 24 = 72

-----------

To help confirm this, we can list out the multiples of each

• multiples of 18 are: 18, 36, 54, 72, 90, ...
• multiples of 24 are: 24, 48, 72, 96, ...

We see that 72 is the lowest common multiple. This is the final answer because each station will play the same song 72 minutes apart.

The stations play the same song at 3 PM. Then 72 minutes later (4:12 PM), the same song is played again on both stations at the same time. Then at 5:24 PM, another 72 minute gap, is when the same song is played again at the same time. And so on.

----------

Side note: 72 minutes = 60 min + 12 min = 1 hr, 12 min

Answer 2

72 minutes until they play again

Step-by-step explanation:

18+18+18+18=72

24+24+24=72