For a two dimensional cyclic quotient singularity of type 1/r(1,a), the self-intersection numbers of the exceptional divisor of a minimal resolution corresponds to the coefficients of the Hirzebruch-Jung continued fraction for r/a. In toric geometry, a minimal resolution is characterized as a subdivision of a fan using only lattice points of Hilbert basis. In this talk, I will introduce n-dimensional complete coprime cyclic quotient singularities. It has a good resolution which is obtained by subdivision using only points of Hilbert basis. Moreover, there is one to one correspondence between exceptional divisors of this resolution and the multidimensional continued fraction.