Find the HCF of $288$ and $540$ by prime factorisation. Hence, find their LCM and verify that $\text{HCF} \times \text{LCM} = \text{Product of the two numbers}$.
Step-by-Step Solution
Key Concept: $288 = 2^5 \times 3^2$, $540 = 2^2 \times 3^3 \times 5$. $\text{HCF} = 36$, $\text{LCM} = 4320$.
Prime factorisation: $288 = 2^5 \times 3^2$, $540 = 2^2 \times 3^3 \times 5$. [1.5 Marks]
$\text{HCF} = 2^2 \times 3^2 = 36$. [1.0 Mark]
$\text{LCM} = 2^5 \times 3^3 \times 5 = 32 \times 27 \times 5 = 4320$. [1.0 Mark]
Verification:
$\text{LHS} = \text{HCF} \times \text{LCM} = 36 \times 4320 = 155520$.
$\text{RHS} = 288 \times 540 = 155520$.
$\text{LHS} = \text{RHS}$. Verified! [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Prime factorisation: 1.5 Marks
Evaluating HCF $= 36$: 1.0 Mark
Evaluating LCM $= 4320$: 1.0 Mark
Verifying product equality ($155,520$): 1.5 Marks
Correct Answer: