Patsy has cheerleading practice every fourth day. She wants to be in the school play, but they have practice every sixth day. If both start on September 5th, what would be the next date she has to choose between cheerleading and play practice? Show your work and explain.

what I put is: The LCM of 6 and 4 is 12, so on the 12th of September she will have to choose between play and cheerleading practice.

am I correct?

yes

you are correct about the 12 day period ... but

..."If both start on September 5th..."

the question asks for the date of the next conflict

Yes, you are correct! The LCM (Least Common Multiple) of 6 and 4 is indeed 12. This means that the next date where both cheerleading practice (every 4 days) and play practice (every 6 days) coincide will be on the 12th of September. On that day, Patsy will have to choose between attending cheerleading practice or play practice.

Yes, you are correct! To determine the next date Patsy has to choose between cheerleading and play practice, we need to find the least common multiple (LCM) of 6 and 4. Here's how you can find the LCM:

Step 1: List the multiples of each number:
Multiples of 6: 6, 12, 18, 24, 30, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...

Step 2: Identify the common multiples in both lists:
The common multiples of 6 and 4 are 12, 24, 36, ...

Step 3: Determine the smallest common multiple:
The smallest common multiple is 12. So, on the 12th of September, Patsy will have to decide between cheerleading and play practice.

Great job on finding the LCM and providing the correct answer!