which is the number that is divided by 7,9, and 11 to get remainder as 1,2,and 3.

let the number be n. if n is divided by 7 it leaves remainder 1.

therefore  .........(1)

if n is divided by 9 it leaves remainder 2.

if n is divided by 11 it leaves remainder 3. 

N = 1(mod 7) = 2(mod 9) = 3(mod 11)

from (1) nN= 7p+1 where p is an inetger.

from (2):

  where m is an integer.

the number 

 where n is an integer.

since here we are trying to find the smallest number, so we will write n =0

thus the required number = 344