Question

In the set of consecutive integers from 15 to 30 inclusive, two integers are multiples of both 3 and 5. How many integers in this set are multiples of neither 3 nor 5?

Answer 1

Number of integers ,multiples of neither 3 nor 5 = 8

Explanation:

Given:

Integers

[15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]

Total number of integer = 16

Find:

Number of integers ,multiples of neither 3 nor 5?

Computation:

Common multiples of both 3 and 5 = 15 ,30 = 2 integers

Multiply of 3 = 18,21,24,27 = 4 integers

Multiply of 5 = 20,25 = 2 integers

Number of integers ,multiples of neither 3 nor 5 = Total number of integer - Common multiples of both 3 and 5 - Multiply of 3 - Multiply of 5

Number of integers ,multiples of neither 3 nor 5 = 16 - 2 - 4 - 2

Number of integers ,multiples of neither 3 nor 5 = 8