LCM New Year

Consider all possible natural numbers a,b,c,x,y,a, b, c, x, y, and zz such that
1) LCM(a,b,c)=LCM(x,y,z)=2015, LCM(a,b,c) = LCM(x,y,z) = 2015,
2) both a+b+ca+b+c and x+y+zx+y+z are perfect squares,
3) a,b,ca, b, c are distinct,
4) x,y,z x, y, z are distinct.

Find the maximum value of abcxyz. a - b - c - x - y - z.

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