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You can express $8, 9, 6, 4, 2, 5$ and $7$ as $2^3, 3^2, 2 \times 3, 2^2, 2, 5$ and $7$.
That means the LCM must contain $2^3, 3^2, 5$ and $7$ to ensure that it is a multiple of all the numbers.
So the LCM is $2^3 \times 3^2 \times 5 \times 7 = 2520$.
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.