What is the LCM of 24 and \( 8 ? \)

To find the **Least Common Multiple (LCM)** of 24 and 8, follow these steps: ### Step 1: Prime Factorization Break down each number into its prime factors. - **24** - \( 24 = 2 \times 12 \) - \( 12 = 2 \times 6 \) - \( 6 = 2 \times 3 \) - So, \( 24 = 2^3 \times 3 \) - **8** - \( 8 = 2 \times 4 \) - \( 4 = 2 \times 2 \) - So, \( 8 = 2^3 \) ### Step 2: Identify the Highest Powers of All Primes For each prime number present in the factorizations, take the highest power: - **Prime 2:** The highest power is \( 2^3 \) (common to both 24 and 8). - **Prime 3:** The highest power is \( 3^1 \) (only in 24). ### Step 3: Multiply These Highest Powers Together \[ \text{LCM} = 2^3 \times 3 = 8 \times 3 = 24 \] ### Conclusion The **LCM of 24 and 8 is 24**. This means that 24 is the smallest number that both 24 and 8 can divide without leaving a remainder.