M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9?

M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively.
Now as 4-2 =5-3 =6-4 =7-5 =2
M will be of the form :k LCM(4,5,6,7) -2=420k-2
M will be 418,838,1258....
Now the largest 4 digit number of the series will be : 418+(n-1)*422<10,000
 so we get                                                                        418+420(22) =9658
Now 9658 mod 9 = 28 mod 9 =1