1. The problem is to find the least common multiple (LCM) of the numbers 9, 12, and 40. 2. First, find the prime factorization of each number: - $9 = 3^2$ - $12 = 2^2 \times 3$ - $40 = 2^3 \times 5$ 3. To find the LCM, take the highest power of each prime factor that appears: - For 2, the highest power is $2^3$ (from 40) - For 3, the highest power is $3^2$ (from 9) - For 5, the highest power is $5^1$ (from 40) 4. Multiply these highest powers together: $$LCM = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5$$ 5. Calculate the product: $$8 \times 9 = 72$$ $$72 \times 5 = 360$$ 6. Therefore, the LCM of 9, 12, and 40 is $360$.