1. **Problem Statement:** Find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of the numbers 18, 20, and 10. 2. **Formulas and Rules:** - The HCF (also called GCD) of numbers is the greatest number that divides all of them without leaving a remainder. - The LCM of numbers is the smallest number that is a multiple of all of them. - To find HCF, we can use prime factorization and take the product of the lowest powers of common primes. - To find LCM, we take the product of the highest powers of all primes appearing in the factorizations. 3. **Prime Factorization:** - 18 = $2 \times 3^2$ - 20 = $2^2 \times 5$ - 10 = $2 \times 5$ 4. **Find HCF:** - Common prime factors: 2 - Lowest power of 2 in all numbers is $2^1$ - So, HCF = $2$ 5. **Find LCM:** - Take highest powers of all primes: - For 2: highest power is $2^2$ - For 3: highest power is $3^2$ - For 5: highest power is $5^1$ - LCM = $2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180$ **Final Answer:** - HCF = 2 - LCM = 180