Question

Which of the following number pairs have a least common multiple that is greater than 15 and less than 25? Select three that apply.

A) 4 and 7
B) 3 and 6
C) 5 and 8
D) 2 and 9
E) 6 and 10

Answer 1

The number pairs A), C), and E) have a least common multiple that is greater than 15 and less than 25.

Step-by-step explanation:

To determine the least common multiple (LCM) of a pair of numbers, we need to find the smallest number that is a multiple of both numbers. We can use prime factorization to find the LCM. Let's analyze each pair of numbers:

1. A) 4 and 7: The prime factorization of 4 is 2^2 and the prime factorization of 7 is 7. The LCM is 2^2 * 7 = 28, which is greater than 15 and less than 25.
2. C) 5 and 8: The prime factorization of 5 is 5 and the prime factorization of 8 is 2^3. The LCM is 2^3 * 5 = 40, which is greater than 15 and 25.
3. E) 6 and 10: The prime factorization of 6 is 2 * 3 and the prime factorization of 10 is 2 * 5. The LCM is 2 * 3 * 5 = 30, which is greater than 15 and less than 25.

Therefore, the number pairs A), C), and E) have a least common multiple that is greater than 15 and less than 25.