Question
Baldwin's apartment complex and the Columbia Commons apartment complex have the same number of apartments. However, Baldwin's apartment complex is built in groups of 2 apartments, while the Columbia Commons apartment complex is built in clusters of 6. What is the smallest number of apartments could each complex have
Answers
GPT-4o mini
To find the smallest number of apartments that Baldwin's apartment complex and the Columbia Commons apartment complex could each have, we need to determine the least common multiple (LCM) of the two cluster sizes: 2 (Baldwin's) and 6 (Columbia Commons).
To calculate the LCM of 2 and 6, we can follow these steps:
1. List the multiples of each number:
- Multiples of 2: 2, 4, 6, 8, 10, 12, ...
- Multiples of 6: 6, 12, 18, 24, ...
2. Identify the smallest common multiple from these lists:
- The first common multiple is 6.
Therefore, the smallest number of apartments each complex could have is **6**.
This means Baldwin's apartment complex would have 6 apartments (which can be made from 3 groups of 2) and Columbia Commons apartment complex would also have 6 apartments (which can be made from 1 cluster of 6).
To calculate the LCM of 2 and 6, we can follow these steps:
1. List the multiples of each number:
- Multiples of 2: 2, 4, 6, 8, 10, 12, ...
- Multiples of 6: 6, 12, 18, 24, ...
2. Identify the smallest common multiple from these lists:
- The first common multiple is 6.
Therefore, the smallest number of apartments each complex could have is **6**.
This means Baldwin's apartment complex would have 6 apartments (which can be made from 3 groups of 2) and Columbia Commons apartment complex would also have 6 apartments (which can be made from 1 cluster of 6).