4. (5 points) If the natural number $N$ can be expressed as the sum of 3 consecutive natural numbers, the sum of 11 consecutive natural numbers, and the sum of 12 consecutive natural numbers, then the minimum value of $N$ is $\qquad$. (Note: The smallest natural number is 0)
【Answer】Solution: The natural number $N$ can be expressed as the sum of 3 consecutive natural numbers. Since 3 and 11 are odd numbers,

$N$ can be divided by 3 and 11, which means it can be divided by 33;
The sum of an even number of consecutive natural numbers is equal to the average of the middle two numbers multiplied by the number of terms, so $N$ equals an integer plus 0.5 and then multiplied by 12,

which means it leaves a remainder of 6 when divided by 12, and this can also be divided by 33, so the smallest possible number is 66.

Therefore, the answer is: 66.