turkey-yks 2017 Q7

turkey-yks · Other · lys1-math Number Theory GCD, LCM, and Coprimality
Let $a$ and $b$ be distinct positive integers such that LCM(a,b) equals a prime number.
Accordingly,\ I. $a$ and $b$ are coprime numbers.\ II. The sum $a + b$ is an odd number.\ III. The product $\mathrm{a} \cdot \mathrm{b}$ is an odd number.
Which of the following statements are always true?\ A) Only I\ B) Only II\ C) Only III\ D) I and II\ E) II and III
Let $a$ and $b$ be distinct positive integers such that LCM(a,b) equals a prime number.

Accordingly,\
I. $a$ and $b$ are coprime numbers.\
II. The sum $a + b$ is an odd number.\
III. The product $\mathrm{a} \cdot \mathrm{b}$ is an odd number.

Which of the following statements are always true?\
A) Only I\
B) Only II\
C) Only III\
D) I and II\
E) II and III