Kevin, yone, and Miroki work part time at the YMCA in Kamloops Kevin works every second day Yone works every third day Miroki works every fourth day. Today they worked together. When will they work together again? Explain how you know!

Answer 1

To determine when Kevin, Yone, and Miroki will work together again after today, we need to find the least common multiple (LCM) of their working frequencies.

1. Kevin's schedule: Works every 2 days.
2. Yone's schedule: Works every 3 days.
3. Miroki's schedule: Works every 4 days.

Now, we will calculate the LCM of 2, 3, and 4.

Step 1: Factor each number into primes

• 2 = \(2\)
• 3 = \(3\)
• 4 = \(2^2\)

Step 2: Identify the highest powers of each prime factor

• The highest power of 2 is \(2^2\) (from 4).
• The highest power of 3 is \(3^1\) (from 3).

Step 3: Calculate the LCM LCM = \(2^2 \times 3^1 = 4 \times 3 = 12\)

Thus, Kevin, Yone, and Miroki will all work together again in 12 days.

Conclusion: They will work together again in 12 days.