答案：B

解析：

The number of positive integer multiples of 3 that are less than or equal to 100 is 99 divided by 3 equals 33. The number of positive integer multiples of 5 that are less than or equal to 100 is 100 divided by 5 equals 20. The multiples of both 3 and 5 are the multiples of 3 times 5 equals 15, and there are 90 divided by 15 equals 6 positive integers less than 100 that are multiples of 15. The multiples of both 3 and 5 are counted twice when counts of the multiples of 3 and the multiples of 5 are added together, so the number of positive integers less than or equal to 100 that are multiples of 3 or multiples of 5 or multiples of both 3 and 5 is 33 plus 20 minus 6 equals 47.