2018/002) Find the GCD of all the even numbers formed from permutation of $1,2,3,4,5,6$

Each of the number is divisible by 6.
Let us take 2 number 123546, 123564
Let us find the GCD of the same
$GCD(123546,123564) = GCD(123546,123464-123546)$
$=GCD(123546,18) = GCD(6863 * 18+12,18) = GCD(12,18) = 6$
hence from above GCD = 6