Singularities of weighted projective plane

Question

Let $a,b,c$ be mutually relatively prime positive integers, and let $\Bbb CP^2(a,b,c)$ be the weighted projective plane defined by the quotient space $\Bbb C^3-\{0\}/(z_1,z_2,z_3)\sim (\lambda^a z_1,\lambda^b z_2,\lambda^c z_3)$ for $\lambda\in \Bbb C-\{0\}$. $X=\Bbb CP^2(a,b,c)$ is a complex manifold with three singular points $p_1=[1,0,0], p_2=[0,1,0], p_3=[0,0,1]$. According to https://en.wikipedia.org/wiki/Weighted_projective_space, the only singularities of weighted projective plane are cyclic quotient singularities of the form $\Bbb C^2/G$ where $G\subset GL(2,\Bbb C)$ is cyclic. So, near the points $p_1,p_2,p_3$, $X$ must be a cone on lens space $L(a,a'), L(b,b'), L(c,c')$. Can we determine the integers $a',b',c'$? Or is there a reference about concerning singularities of weighted projective planes?