Generating mapping class group by two torsion elements

We prove that the mapping class group of a closed connected orientable surface of genus $g$ is generated by two elements of order $g$ for $g\ge 6$. Moreover, for $g\ge 7$ we found a generating set of two elements, of order $g$ and $g^{\mathrm{\prime }}$ which is the least divisor of $g$ such that $g^{\mathrm{\prime }}>2$. Furthermore, we proved that it is generated by two elements of order $g\mathrm{/}\gcd (g,k)$ for $g\geq 3k^2+4k+1$andanypositiveinteger$k$.