The relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers can be expressed using the following formula:

$\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$

Explanation:

• HCF (or GCD) of two numbers is the largest number that divides both numbers.
• LCM of two numbers is the smallest number that is divisible by both numbers.

The product of the HCF and LCM of two numbers equals the product of the numbers themselves.

Example:

Consider two numbers, 12 and 18.

1. HCF(12, 18) = 6
2. LCM(12, 18) = 36

Now, according to the relationship:

$6 \times 36 = 12 \times 18$

This gives:

$216 = 216$

This confirms the relationship holds true.

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Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you find the HCF and LCM using prime factorization?
2. Can this relationship be extended to more than two numbers?
3. How do HCF and LCM relate when one number is a multiple of the other?
4. Can the HCF of two numbers be greater than their LCM?
5. What are real-world applications of HCF and LCM?

Tip: When finding both HCF and LCM using prime factorization, the HCF is obtained by taking the lowest powers of common factors, and the LCM is obtained by taking the highest powers of all factors.