1. The problem is to find the formulas for the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of two numbers. 2. The HCF (also called GCD - Greatest Common Divisor) of two numbers is the largest number that divides both numbers exactly. 3. The LCM of two numbers is the smallest number that is a multiple of both numbers. 4. Important rule: For any two positive integers $a$ and $b$, the product of their HCF and LCM equals the product of the numbers themselves. 5. This can be written as the formula: $$\text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b$$ 6. From this, if you know one of HCF or LCM, you can find the other: $$\text{LCM}(a,b) = \frac{a \times b}{\text{HCF}(a,b)}$$ $$\text{HCF}(a,b) = \frac{a \times b}{\text{LCM}(a,b)}$$ 7. To find HCF, you can use the Euclidean algorithm which repeatedly applies: $$\text{HCF}(a,b) = \text{HCF}(b, a \bmod b)$$ until $b=0$. 8. To find LCM, once HCF is known, use the formula above. This completes the explanation of formulas for HCF and LCM.