Addition&Subtraction

so im taking an online algebra course:

and when its reached the subject of adding fraction (in this case three)

the instructor explains that we need to find the lowest common denominator.

And he shows to ways to do it the first one is simply to make a list of all the multiples

of each denominator and then find locate the lowest common multiple.

The second is is to multiply all the denominators and then use the result as the common denominator,

it gave me somewhat of a head scratchier.

Witch time is the best to use each method?

Multiplication

can any one provide me with a good way to multiply big fractions without a calculator?

Thanks!