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If the largest prime factor of m is 13 and the largest prime factor of n is 11, what is the largest number of unique prime factors that mn could have?

Correct Answer:

**B**The first prime numbers are: 2, 3, 5, 7, 9, 11, 13, 17, 19

- The factors of m can include any primes up to and including 13, so at most, m can have 2, 3, 5, 7, 11, and 13 as prime factors. Similarly, n can have at most 2, 3, 5, 7, and 11 as prime factors.
- The prime factors of mn are primes that are factors of m or n, so they could be 2, 3, 5, 7, 11, and 13 at most. This gives 6 prime factors.
- The answer is B