Let ${ a }_{ 1 }>{ a }_{ 2 }>0$ and ${ a }_{ n+1 }=\sqrt { \left( { a }_{ n }{ a }_{ n-1 } \right) }$ ; $n\ge 2$. If $\displaystyle{\lim_{ n\rightarrow \infty }{ a }_{ n }}=l{ a }_{ 1 }^{ m }{ a }_{ 2 }^{ n }$, then what is the value of $l+m+n?$

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