For two positive integers, HCF × LCM equals:

For any two positive integers $a$ and $b$, there is a fundamental mathematical property relating their Highest Common Factor (HCF) and Least Common Multiple (LCM). ### Step-by-Step Explanation: 1. **Define the Property**: The relationship is defined by the formula: $$\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$$ 2. **Verification with an Example**: Let $a = 4$ and $b = 6$. - Factors of $4$: $1, 2, 4$ - Factors of $6$: $1, 2, 3, 6$ - $\text{HCF}(4, 6) = 2$ - Multiples of $4$: $4, 8, 12, 16...$ - Multiples of $6$: $6, 12, 18...$ - $\text{LCM}(4, 6) = 12$ 3. **Check the Product**: - $\text{HCF} \times \text{LCM} = 2 \times 12 = 24$ - $\text{Product of numbers} = 4 \times 6 = 24$ Since $24 = 24$, the property holds true. Therefore, the product of HCF and LCM is equal to the product of the two numbers.