10. (10 points) On a circle, there are 70 points. Choose one of these points and label it 1, then label the point two points clockwise from it as 2, the point three points clockwise from it as 3, and the point four points clockwise from it as 4, and continue this operation until 1, 2, 3, ..., 2014 are all marked on the points. Each point may be labeled with more than one number. What is the smallest integer marked on the point that is labeled 2014? $\qquad$
【Analysis】First, according to the sum formula of an arithmetic sequence, the sum of $1, 2, 3, \cdots, 2014$ is 2029105; then consider the 70 points on the circumference as equally divided points, since $2029105 \div 70=28987 \cdots 15$, so 2014 falls on the 15th point on the circumference. Given that $15=1+2+3+4+5$, the smallest integer is 5, so the smallest integer marked on the point labeled 2014 is 5. According to this, solve the problem.

【Solution】Solution: $1+2+3+\cdots+2014$
$$
\begin{array}{l}
=(1+2014) \times 2014 \div 2 \\
=2015 \times 2014 \div 2 \\
=2029105
\end{array}
$$

Since $2029105 \div 70=28987 \cdots 15$,
2014 falls on the 15th point on the circumference,
and since $15=1+2+3+4+5$, the smallest integer is 5,
so the smallest integer marked on the point labeled 2014 is 5.
Answer: The smallest integer marked on the point labeled 2014 is 5.
Therefore, the answer is: 5.