**Answer**: (C) 9658

**Explanation: **LCM(4, 5, 6, 7) = 420

Now, the largest 4 digits number = 9999

Dividing, 9999 by 499 we have 339 as remainder. Therefore the largest 4 digits number that is divisible by 4, 5, 6 and 7 is = (9999 – 339) = 9660

Also, (4 – 2) = (5 – 3) = (6 – 4) = (7 – 5) = 2

Hence the required number = 9660 – 2 = 9658