There is no such thing as a most common denominator.
A common denominator is 75.
A common denominator, though not the least, is 7500.
It is any multiple of 75.
It is 75.
LCD(75, 275) = 825
The common denominator of any two or more whole numbers will always be 1.
If I wanted to be nasty about it, I would say 1, because the least common denominator of 45/1 and 75/1 is 1. The least common denominator of two fractions is the least common multiple of their denominators. I presume you are asking for the least common multiple of 45 and 75, which is 225.
525
1200
975
3000
The greatest common denominator, like the greatest common multiple, is infinite.