1959 AHSME Problem 42

Given three positive integers a,b, and c. Their greatest common divisor is D; their least common multiple is M. Then, which two of the following statements are true? \begin{array}{l} \text{(1)}\ \text{the product MD cannot be less than abc} \qquad \\ \text{(2)}\ \text{the product MD cannot be greater than abc}\qquad \\ \text{(3)}\ \text{MD equals abc if and only if a,b,c are each prime}\qquad \\ \text{(4)}\ \text{MD equals abc if and only if a,b,c are each relatively prime in pairs} \text{ (This means: no two have a common factor greater than 1.)} \end{array} \textbf{(A)}\ 1,2 \qquad\textbf{(B)}\ 1,3\qquad\textbf{(C)}\ 1,4\qquad\textbf{(D)}\ 2,3\qquad\textbf{(E)}\ 2,4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.