1. **State the problem:** Find the least common multiple (LCM) of 5 and 9. 2. **Formula and rules:** The LCM of two numbers is the smallest positive integer that is divisible by both numbers. 3. **Step-by-step solution:** - Prime factorize each number: - 5 is prime, so its factors are $5$ - 9 can be factored as $3^2$ - To find the LCM, take the highest powers of all prime factors: - From 5: $5^1$ - From 9: $3^2$ - Multiply these together: $$\text{LCM} = 5^1 \times 3^2 = 5 \times 9 = 45$$ 4. **Explanation:** The LCM is the smallest number that both 5 and 9 divide into without remainder. Since 5 and 9 share no common prime factors, the LCM is simply their product. **Final answer:** The LCM of 5 and 9 is $45$.