E is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in E?
I. 9
II. 15
III. 27 Choose the correct choice from the following answers
A) I only  B) II only  C) I and II only  D) I and III only  E) I, II, and III
Ans: C   E-&gt;{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3   means x must contain 3^2 and 5^2   so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25   but 27 is not a divisor because it can't divide 9*25 fully.   so Ans : I and II only
<result>C</result>
E is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in E?
I. 9
II. 15
III. 27