How many integers between 1-100 are divisible by 3 or 5 or 7?

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 = 33

5 10 20 25 35 40 50 55 65 70 80 85 95 100 = 14

7 14 28 49 56 77 91 98 = 8

So 55 numbers are divisible by 3 or 5 or 7.