Try gcd(30/7, 8/42) your method gives 2/42 or 1/21
Try gcd(30/7, 4/21) your method gives 2/21
8/42 = 4/21 but 1/21 does not equal 2/21
You can fix this if you reduce all fractions before computing but that does not gaurantee there are no other difficulties with your method.
I invite everyone to test my method in post #7