  In this paper, we study how the roots of the so-called Kac polynomial $W_n(z)
= \sum_{k=0}^{n-1} \xi_k z^k$ are concentrating to the unit circle when its
coefficients of $W_n$ are independent and identically distributed
non-degenerate real random variables. It is well-known that the roots of a Kac
polynomial are concentrating around the unit circle as $n\to\infty$ if and only
if $\mathbb{E}[\log( 1+ |\xi_0|)]<\infty$. Under the condition of
$\mathbb{E}[\xi^2_0]<\infty$, we show that there exists an annulus of width
$\mathrm{O}(n^{-2}(\log n)^{-3})$ around the unit circle which is free of roots
with probability $1-\mathrm{O}({(\log n)^{-{1}/{2}}})$. The proof relies on the
so-called small ball probability inequalities and the least common denominator.
