7. (3 points) There are 5 different positive integers, and the product of any two of them is a multiple of 12. The minimum value of the sum of these 5 numbers is $\qquad$ .
【Solution】Solution: Since $12=2 \times 6=3 \times 4$, the two numbers could be $2, 6$ or $3, 4$;
(1) If the smallest two numbers are 2 and 6, then to meet the condition, the next three numbers must be divisible by 6, which are
12, 18, and 24, with their sum being 62;
(2) If the smallest two numbers are 3 and 4, then to meet the condition, the next three numbers must be divisible by 12, which are
12, 24, and 36, with their sum being 79;
Therefore, the minimum sum of these 5 numbers is 62.
The answer is: 62.