A class can make equal teams of 5 for basketball, or equal teams of 6 for volleyball. Each student in the class was on a team. How many students might be in the class? Please explain.
57
There will be 50 kids
To find the possible number of students in the class, we need to find the least common multiple (LCM) of 5 and 6 because all the students in the class must be divided equally into teams for both basketball and volleyball.
To find the LCM of 5 and 6, we can start by listing their multiples:
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
From the above list, we can see that the first common multiple of 5 and 6 is 30. So, a possible number of students in the class could be 30.
However, there could be other possible numbers that are multiples of the LCM (30) as well. We can continue the list:
Multiples of 30: 30, 60, 90, 120, 150, 180, ...
So, any positive integer multiple of 30, such as 30, 60, 90, 120, etc., is also a possible number of students in the class.
Therefore, the class could have any number of students that is a positive integer multiple of 30.
What is the least common multiple for 5 and 6?
5, 10, 15, 20, 25, 30, 35, 40
6, 12, 18, 24, 30, 36, 42