7. (5 points) A natural number $n$ greater than 0 is a multiple of 3, and $3 n$ is a multiple of 5, then the minimum value of $n$ is
7. (5 points) For a natural number $n$ greater than 0, $n$ is a multiple of 3, and $3 n$ is a multiple of 5, then the minimum value of $n$ is $\qquad$ 15 .

【Solution】Solution: $3 n$ is a multiple of 5, so the last digit of $3 n$ must be 0 or 5.
Since $n$ is a natural number greater than 0 and is a multiple of 3,
the smallest value of $3 n$ is 45
$3 n=45$
$$
n=15
$$

Therefore, when $n$ is at least 15, $n$ is a multiple of 3, and $3 n$ is a multiple of 5.
Answer: The minimum value of $n$ is 15.
So the answer is: 15 .