If a and b are two distinct positive integers, what is the largest number that leaves no remainder when it divides a...

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Source: E-GMAT

If a and b are two distinct positive integers, what is the largest number that leaves no remainder when it divides a and b?

1) a and b can be written as 8x and 8y respectively, where x and y are distinct integers with no common prime factors
2) a is equal to 24 and both a and b are divisible by the same perfect cubes

The OA is A