Let p =x^2 y^3 z^n and q =x^3 y^m z^2, where x, y, z are prime numbers. If LCM ( p, q )=x^3 y^4 z^3, then the value of (2 m +3 n ) is

Let $\displaystyle \mathrm{p}=x^{2} \mathrm{y}^{3} \mathrm{z}^{\mathrm{n}}$ and $\displaystyle \mathrm{q}=x^{3} \mathrm{y}^{\mathrm{m}} \mathrm{z}^{2}$, where $\displaystyle x, \mathrm{y}, \mathrm{z}$ are prime numbers. If LCM $\displaystyle (\mathrm{p}, \mathrm{q})=x^{3} \mathrm{y}^{4} \mathrm{z}^{3}$, then the value of $\displaystyle (2 \mathrm{m}+3 \mathrm{n})$ is