NCERT Class X Chapter 1: Real Numbers Example 3

NCERT Class X Chapter 1: Real Numbers Example 3

Question:

Find the HCF of 96 and 404 by the prime factorisation method. Hence, find their LCM.

Given:

Numbers: 96 and 404

To Find:

HCF and LCM of 96 and 404 using the prime factorisation method.

Formula:

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

Solution:

Step 1: Find the prime factorisation of 96.

$$ 96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 $$

Step 2: Find the prime factorisation of 404.

$$ 404 = 2 \times 2 \times 101 = 2^2 \times 101 $$

Step 3: Find the HCF by taking the lowest power of common prime factors.

Common prime factor: 2

Lowest power of 2 in both numbers: \(2^2\)

$$ \text{HCF}(96,\,404) = 2^2 = 4 $$

Step 4: Use the formula to find the LCM.

$$ \text{HCF} \times \text{LCM} = 96 \times 404 $$ $$ 4 \times \text{LCM} = 38784 $$

Step 5: Calculate the LCM.

$$ \text{LCM} = \frac{38784}{4} = 9696 $$

Result:

\(\text{HCF}(96,\,404) = 4\)
\(\text{LCM}(96,\,404) = 9696\)

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