# 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