jmc

The common difference in this arithmetic sequence is $987-1000=-13$, so the $n^{\text{th}}$ term in this sequence is $1000-13(n-1)=1013-13n$. This expression is positive if and only if $1013-13n>0$, or $$n<\frac{1013}{13}=77+\frac{12}{13}.$$ Since $n$ must be a positive integer, $n\le 77$. Hence, the least positive integer in this sequence corresponds to the value $n=77$, in which case $1013-13n=1013-13\cdot 77=\boxed{12}$.