What is the product of the LCM and GCD of 24 and 36? Simplify the expression (7/9 + 5/6 - 2/3).

$$24 = 2 \times 12 = 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3^1$$ $$36 = 2 \times 18 = 2 \times 2 \times 9 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2$$

The GCD is found by taking the lowest power of each common prime factor.

$$GCD(24, 36) = 2^{\min(3,2)} \times 3^{\min(1,2)} = 2^2 \times 3^1 = 4 \times 3 = 12$$

The LCM is found by taking the highest power of all prime factors present.

$$LCM(24, 36) = 2^{\max(3,2)} \times 3^{\max(1,2)} = 2^3 \times 3^2 = 8 \times 9 = 72$$

$$Product = LCM(24, 36) \times GCD(24, 36) = 72 \times 12$$ $$Product = 864$$

Alternatively, for any two positive integers $a$ and $b$, $LCM(a, b) \times GCD(a, b) = a \times b$.

$$Product = 24 \times 36 = 864$$

The product is $\boxed{\text{C. } 864}$.

13)

$$(\frac{7}{9} + \frac{5}{6} - \frac{2}{3})$$

Find a common denominator for 9, 6, and 3. The least common multiple (LCM) of 9, 6, and 3 is 18.
Convert each fraction to have a denominator of 18:

$$\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}$$ $$\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}$$ $$\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}$$

$$\frac{17}{18} \times \frac{1}{3} = \frac{17 \times 1}{18 \times 3} = \frac{17}{54}$$

The value of the expression is $\boxed{\text{D. } \frac{17}{54}}$.