On Bounds for the Smallest and the Largest Eigenvalues of GCD and LCM   Matrices
  In this paper, we study the eigenvalues of the GCD matrix $(S_n)$ and the LCM matrix $[S_n]$ defined on $S_n=\{1,2,\ldots,n\}$. We present upper and lower bounds for the smallest and the largest eigenvalues of $(S_n)$ and $[S_n]$ in terms of particular arithmetical functions. 
Ercan Alt{\i}n{\i}\c{s}{\i}k, \c{S}erife B\"uy\"ukk\"ose
math.NT