1. **State the problem:** We have seams every 8 feet and studs every 16 inches on a piece of plywood. We want to find after how many feet or inches a seam and a stud align (occur at the same point). 2. **Convert units:** Since seams are every 8 feet and studs every 16 inches, convert 8 feet to inches to work with the same units. $$8 \text{ feet} = 8 \times 12 = 96 \text{ inches}$$ 3. **Find the least common multiple (LCM):** We want the smallest distance in inches that is a multiple of both 96 inches (seam spacing) and 16 inches (stud spacing). 4. **Calculate LCM:** - Prime factors of 96: $96 = 2^5 \times 3$ - Prime factors of 16: $16 = 2^4$ The LCM takes the highest powers of primes: $$\text{LCM} = 2^5 \times 3 = 32 \times 3 = 96$$ 5. **Interpretation:** The seams and studs align every 96 inches. 6. **Convert back to feet:** $$96 \text{ inches} = \frac{96}{12} = 8 \text{ feet}$$ **Final answer:** Seams and studs align every 8 feet or 96 inches.