Question

In the summer, Sue swims every six days, lifts every four days, and runs every 16 days. She did all these activities today. How many days will she do all three activities again on the same day?

A) 48 days
B) 24 days
C) 96 days
D) 192 days

Answer 1

Sue will next perform all her activities together on the same day in 48 days after finding the least common multiple (LCM) of the activity frequencies. The correct answer choice is B) 24 days.

This correct answer is B)

Step-by-step explanation:

To determine when Sue will next swim, lift, and run all on the same day, we need to find the least common multiple (LCM) of the three activity frequencies: 6 days (swimming), 4 days (lifting), and 16 days (running).

Step-by-step Calculation:

1. First, list the prime factors of each number:
   • 6 = 2 × 3
   • 4 = 22
   • 16 = 24
2. The LCM is calculated by taking the highest power of each prime factor that appears in any of the numbers. Here, that would be 24 (from 16) and 3 (from 6).
3. Therefore, the LCM of 6, 4, and 16 is 24 × 3 = 16 × 3 = 48.

Sue will next swim, lift, and run all on the same day in 48 days. The correct answer is option B) 24 days.

This correct answer is B)