Good thought process! Step II isn't necessary as you could just traverse the arrays from the end instead of the beginning. I like the idea of starting with the smallest array and looking if that value exists, I just had a while loop and decremented one of the 3 counters each time until I reached values that were all the same. This means that I only traverse each array once whereas yours you might traverse the two other arrays for each value that you look at. Here is my for loop:

    //This values reflect what cylinder index we are looking at in each column
    int col1 = 0; 
    int col2 = 0;
    int col3 = 0; 

    //While the heights that we are looking at aren't equal, decrement one
    while( h1[col1] != h2[col2] || h2[col2] != h3[col3] ) 
    {         
        if( h1[col1] > h2[col2] || h1[col1] > h3[col3] )
            col1++;
        else if( h2[col2] > h1[col1] || h2[col2] > h3[col3] )
            col2++;
        else if( h3[col3] > h2[col2] || h3[col3] > h1[col1])
            col3++;
    }

    System.out.println(h1[col1]); //Once they're equal, print this