In order to be able to continue calculating with the least possible, manageable numbers in the course of a calculation, the lowest possible common denominator should be determined. This denominator, also called the main denominator, is the lowest common multiple (LCM) of the two denominators.
Example: Same-named with lowest common denominator
Based on the above example with the fractions 16 and 38, the lowest common multiple of the two denominators 6 and 8 is 24.
So you can only expand the left-hand fraction by 4 instead of, say, 8, and expand the right-hand fraction by 3 instead of, say, 6.
This way you get the fractions with the same denominator
424 and
924 with 24 as the lowest common denominator.