and LCM of the polynomials $$ 6\left(x^{2}+6 x+8\right) $$ and $$ 2 x^{2}-32 $$

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To find the Least Common Multiple (LCM) of the polynomials $$ 6(x^{2} + 6x + 8) $$ and $$ 2x^{2} - 32 $$, we'll follow these steps:

### 1. Factor Each Polynomial

**First Polynomial:**
$$
6(x^{2} + 6x + 8)
$$
Factor the quadratic:
$$
x^{2} + 6x + 8 = (x + 2)(x + 4)
$$
So, the first polynomial becomes:
$$
6(x + 2)(x + 4)
$$

**Second Polynomial:**
$$
2x^{2} - 32
$$
Factor out the common factor:
$$
2(x^{2} - 16) = 2(x - 4)(x + 4)
$$
So, the second polynomial becomes:
$$
2(x - 4)(x + 4)
$$

### 2. Identify Common and Unique Factors

- **Common Factors:** Both polynomials share the factor $$ (x + 4) $$.
- **Unique Factors:**
  - First Polynomial: $$ (x + 2) $$
  - Second Polynomial: $$ (x - 4) $$
- **Numerical Coefficients:** The coefficients are 6 and 2. The LCM of 6 and 2 is 6.

### 3. Construct the LCM

Take the highest power of each distinct factor and multiply by the LCM of the numerical coefficients:
$$
\text{LCM} = 6 \times (x + 2) \times (x + 4) \times (x - 4)
$$

### 4. Final Answer

$$
\boxed{6(x + 2)(x + 4)(x - 4)}
$$
The LCM of the polynomials $$ 6(x^{2} + 6x + 8) $$ and $$ 2x^{2} - 32 $$ is $$ 6(x + 2)(x + 4)(x - 4) $$.

and LCM of the polynomials and

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