Team green meets at the movie every 3 days,team yellow meets at the movie every 2 days,and team red meets at the movie every 4 days. When will all three teams meet at the movie on the same day?
We need to find the first day when all three teams will meet at the movie together.
We can start by listing out the days when each team will meet:
Team green: Day 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60...
Team yellow: Day 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40...
Team red: Day 4, 8, 12, 16, 20, 24, 28, 32, 36, 40...
We can see that the first time all three teams will meet together is on Day 12.
Team green meets on Day 3 and Team yellow meets on Day 6, so they will both meet on Day 6 x 2 = Day 12.
Team red meets on Day 12, so all three teams will meet on Day 12.
Therefore, all three teams will meet at the movie on the same day on Day 12.
When they all become friends with the time-traveling aliens and watch movies in the future!
To find out when all three teams will meet at the movie on the same day, we need to find the least common multiple (LCM) of 3, 2, and 4.
First, let's list the multiples of each number:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, ...
Multiples of 4: 4, 8, 12, 16, 20, ...
As we can see, the smallest number that is common to all three lists is 12. Therefore, all three teams will meet at the movie on the same day after every 12 days.
To find out when all three teams, green, yellow, and red, will meet at the movie on the same day, we need to find the least common multiple (LCM) of 3, 2, and 4. The LCM is the smallest number that is divisible by all the given numbers.
1. Start with the largest number, which is 4. List its multiples: 4, 8, 12, 16, 20, 24, 28, 32, ...
2. Move to the next largest number, which is 3. List its multiples: 3, 6, 9, 12, 15, 18, 21, 24, 27, ...
3. Continue with the smallest number, which is 2. List its multiples: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
4. Look for the first common multiple in all three lists: 12 is the first number that appears in all three lists.
Therefore, all three teams will meet at the movie on the 12th day.