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Let x be the first number in the arithmetic sequence
and y be the difference 

The numbers are:
A,  B  ,  C
x, x+y, x+2y

We add all to check if it is divisible by 3 or 9


Therefore in in the number ABCABC one factor is 3

ABCABC is divisible by 1001 because ABCABC/1001=ABC

Therefore there are two numbers that are always factors of ABCABC which are 3 and 1001, therefore the largest integer that divide all numbers in the form ABCABC is 3*1001 or 3003