// prettified version of what can be found here:
// https://en.wikibooks.org/wiki/Algorithm_Implementation/Strings/Longest_common_subsequence#JavaScript
function LCS(a, b) {
    var m = a.length,
        n = b.length,
        C = [],
        i,
        j;

    for (i = 0; i <= m; i++) C.push([0]);
    for (j = 0; j < n; j++) C[0].push(0);
    for (i = 0; i < m; i++) {
        for (j = 0; j < n; j++) {
            C[i+1][j+1] = a[i] === b[j]
            ? C[i][j]+1
            : Math.max(C[i+1][j], C[i][j+1]);
        }
    }

    return (function bt(i, j) {
        if (i * j === 0) {
            return '';
        }
        if (a[i-1] === b[j-1]) {
            return bt(i-1, j-1) + a[i-1];
        }
        return (C[i][j-1] > C[i-1][j])
                ? bt(i, j-1)
                : bt(i-1, j);
    }(m, n));
}

console.log(LCS('dis a test bra manyo', 'this is a test, brother yo'));