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?

Question

Mathematics

Arturo Mcknight

10 July, 22:58

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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Answers (1)

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Carlos Nash · Answer 1

Since they can be groups of 8 or 12 the minimum number of students will be equal to the least common multiple of 8 and 12.

The least common multiple is the product of the highest occurring primes from the two number prime factorization ...

8=2*2*2 and 12=2*2*3 so the least common multiple will be 2*2*2*3=24

So there must be at least 24 people in the class ...