6. (5 points) The length, width, and height of a rectangular prism (all greater than 1) are three mutually prime natural numbers. If the volume of this rectangular prism is 665, then its surface area is


6. (5 points) The length, width, and height of a rectangular prism (all greater than 1) are three mutually prime natural numbers. If the volume of this rectangular prism is 665, then its surface area is $\qquad$ . $\qquad$
【Solution】Solution: $665=19 \times 7 \times 5$,
Since the length, width, and height (all greater than 1) are three mutually prime natural numbers, the length, width, and height are 19, 7, and 5 respectively,
$$
\begin{aligned}
& (19 \times 7+19 \times 5+7 \times 5) \times 2 \\
= & (133+95+35) \times 2 \\
= & 263 \times 2 \\
= & 526,
\end{aligned}
$$

Answer: Its surface area is 526.
Therefore, the answer is: 526 .