The music teacher can split the class into groups of 8 or 12. Each group will have the same amount of students. What is the smallest number of people that can be at music class?
20 people
24 people
32 people
96 people
The music teacher can split the class into groups of 8 or 12. Each group will have the same amount of students. What is the smallest number of people that can be at music class?
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To find the smallest number of people in the music class that can be divided into groups of 8 or 12, we need to calculate the least common multiple (LCM) of 8 and 12.
1. Factors of 8: 1, 2, 4, 8
2. Factors of 12: 1, 2, 3, 4, 6, 12
The common factors are 1, 2, and 4.
Now, let’s find the LCM:
– The LCM is found by using the highest powers of all prime factors.
– 8 = 2^3
– 12 = 2^2 * 3^1
Taking the highest power, we have:
– (2^3) from 8
– (3^1) from 12
Thus, the LCM = (2^3 * 3^1 = 8 * 3 = 24).
Therefore, the smallest number of people that can be in the music class is 24 people.