16 Find the LCM of 8 and 12 . The LCM is

To find the **Least Common Multiple (LCM)** of 8 and 12, you can use the **prime factorization** method or list the multiples of each number and identify the smallest common one. ### Method 1: Prime Factorization 1. **Factorize each number into primes:** - **8** can be written as \(2^3\) - **12** can be written as \(2^2 \times 3\) 2. **Identify the highest power of each prime number present:** - For the prime number **2**, the highest power is \(2^3\) (from 8). - For the prime number **3**, the highest power is \(3^1\) (from 12). 3. **Multiply these highest powers together:** \[ LCM = 2^3 \times 3 = 8 \times 3 = 24 \] ### Method 2: Listing Multiples 1. **List the multiples of each number:** - **Multiples of 8:** 8, 16, 24, 32, 40, ... - **Multiples of 12:** 12, 24, 36, 48, 60, ... 2. **Identify the smallest common multiple:** - The smallest number that appears in both lists is **24**. ### Conclusion The **LCM of 8 and 12 is 24**. **Answer:** The LCM of 8 and 12 is 24.