Relationship between the numbers and their HCF and LCM — lesson. Mathematics State Board, Class 6.

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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 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.

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7. Relationship between the numbers and their HCF and LCM