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. 2 and 9 b. 3 and 7 c. 4 and 10 d. 5 and 12

Explanation:

Step1: Find LCM of 2 and 9

Prime factors of 2: $2$; Prime factors of 9: $3^2$. LCM is $2\times3^2 = 18$. $15<18<25$.

Step2: Find LCM of 3 and 7

3 and 7 are coprime, LCM is $3\times7 = 21$. $15<21<25$.

Step3: Find LCM of 4 and 10

Prime factors of 4: $2^2$; Prime factors of 10: $2\times5$. LCM is $2^2\times5 = 20$. $15<20<25$.

Step4: Find LCM of 5 and 12

5 and 12 are coprime, LCM is $5\times12 = 60$. $60>25$.

Answer:

A. 2 and 9, B. 3 and 7, C. 4 and 10