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838. Not Coprime

Let $f(N)$ be the smallest positive integer that is not coprime to any positive integer $n \le N$ whose least significant digit is $3$.

For example $f(40)$ equals to $897 = 3 \cdot 13 \cdot 23$ since it is not coprime to any of $3,13,23,33$. By taking the natural logarithm (log to base $e$) we obtain $\ln f(40) = \ln 897 \approx 6.799056$ when rounded to six digits after the decimal point.

You are also given $\ln f(2800) \approx 715.019337$.

Find $f(10^6)$. Enter its natural logarithm rounded to six digits after the decimal point.