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The sum of all positive integers less than 100 that are divisible by 3 is (3 + 6 + 9 + ... + 96 + 99) = 1665. The sum of all positive integers less than 100 that are divisible by 5 is (5 + 10 + 15 + ... + 90 + 95) = 1015. However, we have counted the numbers that are divisible by both 3 and 5 twice, so we need to subtract them once. The numbers that are divisible by both 3 and 5 are (15, 30, 45, 60, 75, 90), and their sum is 315. Therefore, the sum of all positive integers less than 100 that are divisible by 3 or 5 is 1665 + 1015 - 315 = 2365.