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_6_16.png
 
HCF of \(6\) and \(16\) \(=\) \(2\)
 
LCM:
 
LCM_6_16.png
 
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.