Alphabetic Arithmetic!

Number Theory Level pending

Find the smallest positive integer 'a' for which the following set of equations can be satisfied, where every letter stands for a different positive integer less than 1000.

1/a
= 1/b + 1/c
=1/d+ 1/e
= 1/f +1/g
= 1/h + 1/i +1/j
= 1/k + 1/l +1/m
= 1/n + 1/p +1/q
= 1/r + 1/s +1/t
= 1/u + 1/v +1/w
= 1/x + 1/y +1/z

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