Answer: 72 minutes
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Explanation:
The GCF of 18 and 24 is 6, since this is the largest factor shared between the two numbers
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
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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.
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Side note: 72 minutes = 60 min + 12 min = 1 hr, 12 min
