1. **State the problem:** Find the least common multiple (LCM) of 60 and 72. 2. **Formula and rules:** The LCM of two numbers is the smallest positive integer that is divisible by both numbers. 3. **Step 1: Prime factorization** - 60 = $2^2 \times 3 \times 5$ - 72 = $2^3 \times 3^2$ 4. **Step 2: Take the highest powers of all prime factors** - For 2: highest power is $2^3$ - For 3: highest power is $3^2$ - For 5: highest power is $5^1$ 5. **Step 3: Multiply these highest powers** $$\text{LCM} = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360$$ 6. **Answer:** The LCM of 60 and 72 is **360**.