### Theory:

The product of the two given numbers is equal to the product of their HCF and LCM.

That is, $$\text{Product of given numbers} = \text{HCF} \times \text{LCM}$$
Example:
Find HCF and LCM of two numbers $$6$$ and $$16$$ and verify the relationship between them.

Solution:

HCF:

HCF of $$6$$ and $$16$$ $$=$$ $$2$$

LCM:

LCM of $$6$$ and $$16$$ $$=$$ $$2 \times 2 \times 2 \times 2 \times 3 = 48$$

Relationship between HCF and LCM:

$$\text{Product of given numbers} = \text{HCF} \times \text{LCM}$$

$$6 \times 16 = 2 \times 48$$

$$96 = 96$$

Both are the same.

Hence, the relationship between LCM and HCF is verified.