1. **Problem:** Find the Least Common Multiple (LCM) of the numbers 16, 2, and 45. 2. **Formula and Explanation:** The LCM of a set of numbers is the smallest positive integer that is divisible by all the numbers in the set. 3. **Step 1: Prime Factorization** - 16 = $2^4$ - 2 = $2^1$ - 45 = $3^2 \times 5$ 4. **Step 2: Take the highest powers of all prime factors** - For 2: highest power is $2^4$ - For 3: highest power is $3^2$ - For 5: highest power is $5^1$ 5. **Step 3: Multiply these highest powers to get the LCM** $$LCM = 2^4 \times 3^2 \times 5 = 16 \times 9 \times 5 = 720$$ 6. **Answer:** The LCM of 16, 2, and 45 is **720**. This corresponds to option a. 720.