1. **State the problem:** Simplify and substitute values into the expression $c = 4(x+2y) - 2x$ to find the total cost, where $x$ is the LCM of 6 and 8, and $y$ is the smallest cube number greater than 10. 2. **Find $x$:** The least common multiple (LCM) of 6 and 8 is the smallest number divisible by both. - Prime factors: $6 = 2 \times 3$, $8 = 2^3$ - LCM takes highest powers: $2^3 \times 3 = 8 \times 3 = 24$ So, $x = 24$. 3. **Find $y$:** The smallest cube number greater than 10. - Cubes: $1^3=1$, $2^3=8$, $3^3=27$ - Since 27 is the smallest cube greater than 10, $y = 27$. 4. **Substitute into the expression:** $$c = 4(x + 2y) - 2x$$ $$= 4(24 + 2 \times 27) - 2 \times 24$$ 5. **Simplify inside the parentheses:** $$24 + 2 \times 27 = 24 + 54 = 78$$ 6. **Calculate:** $$c = 4 \times 78 - 48 = 312 - 48 = 264$$ **Final answer:** The total cost of materials is $264$.