Find the HCF and LCM of $96$ and $404$ by the prime factorisation method.
Step-by-Step Solution
Key Concept: Prime factorise both numbers, find $\text{HCF} = \text{product of lowest powers of common primes}$, and $\text{LCM} = \text{product of highest powers of all primes}$.
Prime factorisation: $96 = 2^5 \times 3$, $404 = 2^2 \times 101$. [1.0 Mark]
$\text{HCF}(96, 404) = 2^2 = 4$. [0.5 Mark]
$\text{LCM}(96, 404) = 2^5 \times 3 \times 101 = 32 \times 3 \times 101 = 9696$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Correct prime factorisations of 96 and 404: 1.0 Mark
Correct HCF: 0.5 Mark
Correct LCM: 0.5 Mark
Correct Answer: