The weather is reported every 9 minutes on ABC and every 12 minutes on CBS. Both stations broadcast the weather at 1:30. When are the next three times that the weather will be broadcast at the same time on the two stations?
Why do you think this question might deal with the concept of a Lowest Common Multiple ?
To find the next three times that the weather will be broadcast at the same time on the two stations, we need to find the common multiples of 9 and 12.
The first step is to find the least common multiple (LCM) of 9 and 12. To do this, we can list out the multiples of each number until we find a common multiple.
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, ...
From the lists above, we can see that the least common multiple (LCM) of 9 and 12 is 36, as it is the smallest number that appears in both lists.
Now, we know that the weather will be broadcast at the same time every 36 minutes.
Given that the weather is initially broadcast at 1:30, we can calculate the next three times when the weather will be broadcast at the same time on both stations:
1. First common time: 1:30 + 36 minutes = 2:06
2. Second common time: 2:06 + 36 minutes = 2:42
3. Third common time: 2:42 + 36 minutes = 3:18
Therefore, the next three times when the weather will be broadcast at the same time on ABC and CBS are 2:06, 2:42, and 3:18.