Find the three positive integers puzzle

Find the three positive integers a, b, c where a < b < c, which satisfy:

a*b*c + a*b + b*c + c*a + a + b + c = 2013

Problem Page Coordinator: Stephen Lee CMath MIMA

Mathematics in Education and Industry

Acknowledgement: The IMA are indebted to MEI for sourcing and supplying Mathematics Today with these well-known puzzles.

First published in Mathematics Today (December 2014)