multiply.js

var chunkSize = 5, batchMod = Math.pow(10, chunkSize);

function getChunks(num) {
    var chunks = [],
        count = 0;
    while (true) {
        var length = chunkSize,
            shouldBreak = false;
        var startIndex = num.length - chunkSize * ++count;
        if (startIndex < 0) {
            length = chunkSize + startIndex;
            startIndex = 0;
        }
        if (startIndex === 0) shouldBreak = true;

        chunks.push(parseInt(num.substr(startIndex, length)));

        if (shouldBreak) break;
    }
    return chunks;
}

function multiply(num1, num2) {
    var chunks = getChunks(num1),
        chunks2 = getChunks(num2),
        products = {},
        maxIndex = 0,
        product = '',
        carry = 0;

    for (var i = 0; i < chunks.length; i++) {
        for (var j = 0; j < chunks2.length; j++) {
            var productIndex = i + j;
            if (productIndex > maxIndex) maxIndex = productIndex;
            products[productIndex] = products[productIndex] || [];
            products[productIndex].push(chunks[i] * chunks2[j]);
        }
    }

    for (var i = 0; i <= maxIndex; i++) {
        var sum = products[i].reduce(function(prev, next) {
            return prev + next;
        }, carry);
        
        var value = (sum % batchMod).toString();
        carry = parseInt(sum / batchMod);

        while (i < maxIndex) {
            if (value.length < chunkSize)
                value = '0' + value;
            else
                break;
        }
        product = value + product;

        if (i === maxIndex && carry) product = carry + product;
    }

    return product;
}

console.log(multiply('987654', '123456'));