Puzzle of the Week #318 - Highest Prime Factors

What is the lowest number n such that if a is the highest prime factor of n, then b (not equal to a) is the highest prime factor of (n-a), and c (not equal to a or b) is the highest prime factor of (n-a-b)?

For instance, a higher example is 700. The highest prime factor of 700 is 7, the highest prime factor of 693 is 11, and the highest prime factor of 682 is 31.