how do i get the common denominator for 3 4 5 6 and 7?

Find the LCM of all those numbers. The answer will be the common denominator.

Well, it seems like those numbers are having a hard time agreeing on a common denominator. Maybe you could act as a mediator and remind them that they have something in common—they're all numbers! But if you're looking for a mathematical solution, you could try finding the least common multiple (LCM) of those numbers. That would give you the smallest number that all of them can divide evenly into. Good luck getting those numbers to cooperate!

To find the common denominator for 3, 4, 5, 6, and 7, you can follow these steps:

Step 1: Identify the prime factors of each number.
- For number 3: Prime factorization of 3 is 3.
- For number 4: Prime factorization of 4 is 2 × 2.
- For number 5: Prime factorization of 5 is 5.
- For number 6: Prime factorization of 6 is 2 × 3.
- For number 7: Prime factorization of 7 is 7.

Step 2: List all the prime factors with the highest exponent.
- The prime factors with the highest exponent are: 2^2, 3^1, 5^1, and 7^1.

Step 3: Multiply all the prime factors from Step 2 together.
- Multiply the prime factors: 2^2 × 3^1 × 5^1 × 7^1 = 4 × 3 × 5 × 7 = 420.

So, the common denominator for 3, 4, 5, 6, and 7 is 420.

To find the common denominator for 3, 4, 5, 6, and 7, you need to find the least common multiple (LCM) of these numbers. Here's how you can do it:

1. Prime factorize each number:

- For number 3, it is a prime number, so its prime factorization is 3.
- For number 4, divide it by prime numbers starting from 2: 4 ÷ 2 = 2. Since 2 is also a prime number, the prime factorization of 4 is 2 × 2.
- For number 5, it is a prime number, so its prime factorization is 5.
- For number 6, divide it by prime numbers starting from 2: 6 ÷ 2 = 3. Since 3 is a prime number, the prime factorization of 6 is 2 × 3.
- For number 7, it is a prime number, so its prime factorization is 7.

2. Identify the highest powers of each prime factor:

- The prime factorization of 3 is 3.
- The prime factorization of 4 is 2 × 2. Since we only have one 2 in the prime factorization of 3, we need an additional 2 to match the highest power of 2.
- The prime factorization of 5 is 5. Since we don't have any 5s in the prime factorization of 3 and 4, we need an additional 5.
- The prime factorization of 6 is 2 × 3. Since we already have the highest powers of 2 and 3 accounted for, we don't need any additional factors.
- The prime factorization of 7 is 7. Since we don't have any 7s in the prime factorization of 3, 4, 5, and 6, we need an additional 7.

3. Multiply the identified prime factors:

Multiply the highest powers of the prime factors together: 3 × 2 × 2 × 5 × 7 = 420.

Therefore, the common denominator for 3, 4, 5, 6, and 7 is 420.