How many positive integers less than or equal to 6*7*8*9 solve the system of congruences:

m = 5 (mod 6)

m = 4 (mod 7)

m = 3 (mod 8)

m = 2 (mod 9)

m = 1 (mod 10)

Using CRT + MMI

Product(6, 7, 8, 9)==3,024

m ==2,520k + 11, where k==0,1,2,3........etc.

m==2,520 is smallest integer that satisfies all 5 congruences. The next number would be: 2,520 x 2 ==5,040.