The lowest common denominator of 3/4 and 5/8 is the same as the least common multiple (LCM) of 4 and 8.
Multiples of 4: 4, 8, 12, 16, ...
Multiples of 8: 8, 16, 24, 32, ...
The least common multiple of 4 and 8 is 8.
The lowest common denominator of 3/4 and 5/8 is 8.