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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](https://resources.cdn.yaclass.in/d81b55b8-ff08-4f72-a31c-8bf065a684a0/HCF616pngpng.png)
HCF of \(6\) and \(16\) \(=\) \(2\)
LCM:
![LCM_6_16.png](https://resources.cdn.yaclass.in/eb151585-29c6-4edb-93ab-eabc21e04fb5/LCM616w200pngpng.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.