The following practice questions each offer a different challenge: first, a word problem that indirectly asks you to find the lowest common multiple of two numbers; then, a two-part problem that asks you to find and compare the prime factors for a series of numbers.

## Practice Questions

- Which of the following numbers has the most unique prime factors?
**A.**15**B.**19**C.**27**D.**31 - Tamara goes for a dental checkup every 6 months and gets her eyesight checked every 8 months. If she visited her dentist and her optician this week, how many months will it be until she visits them both in the same week again? __________

## Answers and Explanations

- The correct answer is A.
Find the factors of each answer choice and then pick the one that contains the most unique prime factors.

Choice (A), 15, has the factors 1, 2, 3, 5, and 15, three of which are prime (2, 3, and 5).

Choice (B), 19, has the factors 1 and 19, only one of which is prime (19).

Choice (C), 27, has the factors 1, 3, 9, and 27, only one of which is prime (3).

Choice (D), 31, has the factors 1 and 31, only one of which is prime (31).

Hence, Choice (A) is correct.

- The correct answer is 24 months.
The least common multiple of 6 and 8 is 24, so it will take 24 months before Tamara visits her dentist and her optician in the same week again.