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Start with the smallest multiple of 13 and continue with the next smallest until finding one that fits the specifications.

13, sum of digits is 1 + 3 = 4 which is not prime

26, sum of digits is 2 + 6 = 8 which is not prime

39, sum of digits is 3 + 9 = 12 which is not prime

52, sum of digits is 5 + 2 = 7 which is prime

So, 52 is the smallest positive multiple of 13 for which the sum of its digits is prime.

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Q: What is the smallest positive multiple of 13 for which the sum of its digits is prime?
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