Question 251966
A common denominator could be 7875=75*105
but you rightly pointed out that 15 will go into both 75 and 105
so we divide 7875 by 15 and get 525
so let's why that works

Actually we come up with 525
so to get 525 we multiplied  75*7
and 105* 5
so now we have 4b*7/525a
6*5=30
30/525ab
so we have two fractions 
28b/525a and 30/105ab
the denominators are quite the same yet.
We still have to multiply 28b/525a by b/b
28b^2/525ab and 30/525ab

So from the beginning we could have  found that
105=15*7 and 75=15*5
so they share 15 and need to share 5 and 7
so if we multiply 6/105ab by 5/5 and 4b/75a by 7b/7b
We will have a LCD of 525ab
28b^2/525ab and 30/525ab

Note:
6/105ab was not in its simplest form
Multiply by 1/3 over 1/3 gets us 2/35ab