Gwyn's niece, Angela, has two younger twin siblings, Ann and Ian. To celebrate the twins’ birthday, she asked Gwyn to compose a puzzle in which their names feature. Here it is:

With different letters denoting different digits consistently throughout, and with no leading zeros appearing, the number denoted by GEMINI is exactly divisible by the numbers corresponding to ANN and IAN. These two three-digit numbers have no common factor. The number denoted by ANGIE has digits which increase from left to right.

What number corresponds to ENIGMA?

Note: Adapted from Enigma Number 1681 by Gwyn Owen which appeared in New Scientist on 18 January, 2012