LCS Function Defined
$$\text{LCS}(X _i,Y _j)=\begin{cases} \emptyset & \text{if } i=0 \text{ or } j=0 \\ \text{LCS}(X _{i-1},Y _{j-1}) \hat{\text{ }} x _i & \text{if }i,j>0 \text{ and } x _i = y _i \\ max \text{\textbraceleft} \text{LCS}(X _i,Y _{j-1}, \text{LCS}(X _{i-1},Y _j)\text{\textbraceright} & \text{if } j>0 \text{ and } x _i \ne y _j \end{cases}$$