Question

A high school marching band rehearses with either 6 or 10 members in every line. What is the minimum number of people that can be in the marching band?

a) 60
b) 12
c) 16
d) 30

Answer 1

The minimum number of people that can be in the marching band is 30. Therefore, the minimum number of people that can be in the marching band is 30, as given in option d) 30.

Step-by-step explanation:

In order to find the minimum number of people in the marching band, we need to find the least common multiple (LCM) of 6 and 10. The LCM is the smallest number that is divisible by both 6 and 10 without leaving a remainder.

1. First, let's list the multiples of 6 and 10:
   • Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48...
   • Multiples of 10: 10, 20, 30, 40, 50, 60...
2. We can see that the LCM of 6 and 10 is 30 because it is the smallest number that appears in both lists.

Therefore, the minimum number of people that can be in the marching band is 30, as given in option d) 30.