12. (6 points) Three natural numbers, the largest is 6 more than the smallest, another is their average, and the product of the three numbers is 46332. The largest number is $\qquad$ .
【Solution】Solution: According to the analysis of the problem, we get: $46332=2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 11 \times 13=(2 \times 2 \times 3 \times 3)$ $\times(3 \times 11) \times(3 \times 13)=36 \times 33 \times 39$,

which exactly satisfies the condition that the largest number is 6 more than the smallest: $39-33=6$;
and $(39+33) \div 2=36$,
so the three numbers are $33, 36, 39$, hence the largest number is 39. Therefore, the answer is: 39 .