1. **Stating the problem:** You want to understand how to find the Least Common Multiple (LCM) and Highest Common Factor (HCF) from a word problem. 2. **Formulas and definitions:** - The HCF (or GCD) of two numbers is the greatest number that divides both without leaving a remainder. - The LCM of two numbers is the smallest number that is a multiple of both. 3. **Important rule:** For any two numbers $a$ and $b$, the product of their LCM and HCF equals the product of the numbers: $$\text{LCM}(a,b) \times \text{HCF}(a,b) = a \times b$$ 4. **How to find HCF and LCM from a word problem:** - Identify the two numbers involved. - Use prime factorization or Euclid's algorithm to find the HCF. - Use the formula above or prime factorization to find the LCM. 5. **Example:** Suppose a word problem says two numbers have an HCF of 6 and their product is 180. - Using the formula: $$\text{LCM} = \frac{a \times b}{\text{HCF}} = \frac{180}{6} = 30$$ 6. **Summary:** - Find HCF by common factors or Euclid's algorithm. - Find LCM using the formula or prime factors. - Always check the problem for given values to apply these steps. This method helps solve word problems involving LCM and HCF efficiently.