1. The problem statement, all variables and given/known data Find the two smallest positive integers(different) having the remainders 2,3, and 2 when divided by 3,5, and 7 respectively. 2. Relevant equations 3. The attempt at a solution I got 23 and 128 as my answer. I tried using number theory where I started with 7x +2 as the number, then if divided by 5 the remainder would be 3 so subtract 3 from 7x+2 to get 7x-1 when I use this method and stop there by having x=0,1,2,3,... 3 works 7(3)-1 is divisible by 5 so put 3 in the original 7(3) +2 =23 Then I just used a trial and error method to find 128. Is my answer correct?? I know my procedure is sketchy because I have never been exposed to number theory.