First find the minimum multiple of 3 and 7 plus 2, and then divide it by 5 to verify (the single digit is 3 or 8). If not, add the least common multiple of 3 and 7 to 2 1 in turn, divide it by 5 to verify (as above) until it meets the meaning of the question, and then the number obtained is the smallest positive integer that meets the meaning of the question. If all positive integers are required, add n times to the least common multiple of 3, 5 and 7 105 (n is a positive integer).

Solution: 3*7=2 1

2 1+2=23

The number of units is 3, so 23 is the smallest positive integer that satisfies the meaning of the question.

All positive integers that meet the meaning of the question are: 23+ 105n(n is a positive integer).