Math Question on ABCDEF

Someone posted the following question on the cbox:

Find the 6-digit number ABCDEF such that 7 x ABCDEF = 6 x DEFABC where DEFABC is another 6-digit number. Different letters stand for different single-digit whole numbers.

Solution:
Let
___
ABC = x
___
DEF = y

7 * (1000x + y) = 6 * (1000y + x)
6994x = 5993y
538x = 461y
Clearly, x = 461 and y = 538
Hence the 6-digit number is 461538.