Find the HCF and LCM of $612$ and $1314$ using prime factorisation method.
Step-by-Step Solution
Key Concept: Express both numbers in canonical prime power form.
Stepwise Solution:
Prime factorisation:
$612 = 2^2 \times 3^2 \times 17$
$1314 = 2 \times 3^2 \times 73$. [1.0 Mark]
$\text{HCF}(612, 1314) = 2^1 \times 3^2 = 2 \times 9 = 18$. [0.5 Mark]
$\text{LCM}(612, 1314) = 2^2 \times 3^2 \times 17 \times 73 = 4 \times 9 \times 17 \times 73 = 44676$. [0.5 Mark]
Marking Scheme:
• Correct prime factorisation of 612 and 1314: 1.0 Mark
• Evaluating HCF $= 18$: 0.5 Mark
• Evaluating LCM $= 44676$: 0.5 Mark
Correct Answer: