Samantha is organizing a series of events at her community center. She schedules two recurring activities: a weekly yoga class and a monthly cooking workshop. The yoga class occurs every 7 days, and the cooking workshop occurs every 12 days.

Question

If both events are scheduled to start on the same day, how many days will it be before the yoga class and the cooking workshop fall on the same day again?

(1 point)
Responses

36 days
36 days

42 days
42 days

60 days
60 days

84 days

Answer 1

To find out when both the yoga class and the cooking workshop will fall on the same day again, we need to calculate the least common multiple (LCM) of their schedules: 7 days (yoga class) and 12 days (cooking workshop).

To find the LCM:

1. Prime Factorization:

   • 7 is a prime number: \( 7 = 7^1 \)
   • 12 can be factored into primes: \( 12 = 2^2 \times 3^1 \)

2. Take the highest power of each prime:

   • From 7: \( 7^1 \)
   • From 2: \( 2^2 \)
   • From 3: \( 3^1 \)

3. LCM Calculation: \[ LCM = 2^2 \times 3^1 \times 7^1 = 4 \times 3 \times 7 \]

   Now calculating: \[ 4 \times 3 = 12 \] \[ 12 \times 7 = 84 \]

Thus, the least common multiple of 7 and 12 is 84.

Therefore, both the yoga class and the cooking workshop will fall on the same day again in 84 days.

The answer is 84 days.