Question 1195075
<br>
(1) If it leaves a remainder of 3 when divided by 5, then the units digit is either 3 or 8.<br>
(2) By looking, find the smallest number with units digit 3 or 8 that leaves a remainder of 2 when divided by 3.  You should find that number is 8.<br>
(3) Since the divisors 3 and 5 are relatively prime (they have no common factor), all other numbers that satisfy the two conditions will be found by adding multiples of (3*5)=15 to the first number you found.<br>
So the numbers that satisfy both conditions are 8, 23, 38, 53, ...<br>
ANSWER: 8 and 23<br>