Suppose you want to combine the fractions 13/210 and 29/770. What's the LCD?
Factor both 210 and 770: 3*7*10 and 7*11*10. Form the LCD using the common factors 7 and 10 and the unique factors 3 and 11. The LCD is thus 3(7)(10)(11), or 2310.
Then 13/210 and 29/770 become 143/2310 and 87/2310. We can add these because their denominators are the same.
So the desired LCD is 2310.