7. Four different natural numbers, one of which is an even prime number, the sum of any two is a multiple of 2, the sum of any three is a multiple of 3, and the sum of these four numbers is exactly a multiple of 4. The smallest sum of these 4 numbers is $\qquad$ _.
【Analysis】There is one even prime number, and the only even prime number is 2.
Since the sum of any 2 numbers is a multiple of 2, i.e., even, the other three numbers must all be even.
Since the sum of any 3 numbers is a multiple of 3, the sum of the other three numbers, excluding 2, is a multiple of 3, so the sum of the four numbers divided by 3 leaves a remainder of 2. Since the sum of any 3 numbers is the total sum of the four numbers minus the remaining one, the remainder when any one number is divided by 3 is 2.
Therefore, by the congruence theorem, the difference between any two numbers is both a multiple of 2 and a multiple of 3, meaning the difference between any two numbers is a multiple of 6.
At this point, the four numbers are at least $2, 8, 14, 20$, and the sum of the four numbers is 44, which is a multiple of 4, so the minimum sum of the four numbers is 44.