```


public static int Rec(string s1,string s2,int[][] memo,int i1,int i2){
    if(i1<0||i2<0) return 0;
    if(memo[i1][i2]!=-1) return memo[i1][i2];
    if(s1[i1]==s2[i2]){  memo[i1][i2]=1+Rec(s1,s2,memo,i1-1,i2-1);

      return memo[i1][i2];
    }else
    {
         memo[i1][i2]=Math.Max(Rec(s1,s2,memo,i1,i2-1),Rec(s1,s2,memo,i1-1,i2));

         return memo[i1][i2];
    }
}

public static int commonChild(string s1, string s2)
{

   int[][] dp=new int[s1.Length][];
   for(int i=0;i<s1.Length;i++)
       dp[i]=new int[s2.Length];
   for(int i=0;i<s1.Length;i++){
      for(int j=0;j<s2.Length;j++){
        dp[i][j]=-1;       
      }
   }
   Rec(s1,s2,dp,s1.Length-1,s2.Length-1);

   return dp[s1.Length-1][s2.Length-1];  
}

`

         This is a recusive aproach with memoization.