1. **Problem Statement:** Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers 24 and 36 using factorization. 2. **Formula and Rules:** - The HCF of two numbers is the product of the lowest powers of all prime factors common to both numbers. - The LCM of two numbers is the product of the highest powers of all prime factors present in either number. 3. **Step 1: Prime Factorization** - Factorize 24: $$24 = 2^3 \times 3^1$$ - Factorize 36: $$36 = 2^2 \times 3^2$$ 4. **Step 2: Find HCF** - Take the minimum powers of common primes: - For 2: minimum of 3 and 2 is 2 - For 3: minimum of 1 and 2 is 1 - So, $$\text{HCF} = 2^2 \times 3^1 = 4 \times 3 = 12$$ 5. **Step 3: Find LCM** - Take the maximum powers of all primes: - For 2: maximum of 3 and 2 is 3 - For 3: maximum of 1 and 2 is 2 - So, $$\text{LCM} = 2^3 \times 3^2 = 8 \times 9 = 72$$ 6. **Final Answer:** - HCF of 24 and 36 is **12**. - LCM of 24 and 36 is **72**.