Greg is training for a race he bikes every 2 days and swims every 3 days if he bike and swim today how many days will he pass before he bikes and swims on the same day again the least common multiples of the number of days

To find out how many days will pass before Greg bikes and swims on the same day again, we need to calculate the **least common multiple (LCM)** of the two numbers: 2 days for biking and 3 days for swimming.

### Steps:

1. Greg bikes every 2 days.
2. Greg swims every 3 days.
3. The LCM of 2 and 3 will tell us when these two schedules coincide.

To find the LCM of 2 and 3:
- The prime factorization of 2 is \( 2^1 \).
- The prime factorization of 3 is \( 3^1 \).

The LCM is the product of the highest powers of all prime factors, which is:
\[
LCM(2, 3) = 2^1 \times 3^1 = 6
\]

So, Greg will bike and swim on the same day again in **6 days**.

Would you like further details on how LCM works or any other clarifications?

Here are 5 related questions to expand on this:
1. How is the LCM different from the greatest common divisor (GCD)?
2. What if Greg added running every 4 days—when would all three activities coincide?
3. Can LCM be used in scheduling other events? If so, how?
4. How would we calculate the LCM for larger numbers, like 12 and 15?
5. What happens if the two schedules are already the same?

**Tip:** The LCM helps find the first time multiple repeating events coincide, making it a useful tool in scheduling problems!

Greg is training for a race he bikes every 2 days and swims every 3 days if he bikes and swims today how many days will pass before he bikes and swims on the same day again the least common multiples of the number of days

Discover how to calculate the least common multiple (LCM) when Greg bikes every 2 days and swims every 3 days. This step-by-step solution covers the use of LCM, prime factorization, and key concepts in scheduling problems. Ideal for students in Grades 6-8.

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