What is the LCM of 24 and $$ 8 ? $$

Question

UpStudy AI · Accepted Answer

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.
The LCM of 24 and 8 is 24.

What is the LCM of 24 and