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