In this talk, we introduce some relationships between multi-dimensional continued fractions and Fujiki-Oka resolutions of cyclic quotient singularities. First, we will show a necessary and sufficient condition for the Fujiki-Oka resolutions of Gorenstein abelian quotient singularities to be crepant in all dimensions. Seconds, we introduce complete coprime cyclic quotient singularities. It has a Hilbert basis resolution whose exceptional divisors is contained in any resolution. We show several examples of complete coprime cyclic quotient singularities which satisfy the Euler number of the Fujiki-Oka resolution equal to the order of G. This is a kind of the McKay correspondence.