Let x= a^2 b^3 c^n and y= a^3 b^m c^2, where a, b, c are prime numbers. If LCM of x and y is a^3 b^4 c^3, then the value of m + n is

Let $\displaystyle x=\mathrm{a}^{2} b^{3} \mathrm{c}^{\mathrm{n}}$ and $\displaystyle y=\mathrm{a}^{3} b^{\mathrm{m}} \mathrm{c}^{2}$, where $\displaystyle \mathrm{a}, b, \mathrm{c}$ are prime numbers. If LCM of $\displaystyle x$ and y is $\displaystyle \mathrm{a}^{3} \mathrm{~b}^{4} \mathrm{c}^{3}$, then the value of $\displaystyle \mathrm{m}+\mathrm{n}$ is