Mathematics — Standard (041) — CBSE Class 10 board question

Prime factorisation:

$96 = 2^5 \times 3$

$120 = 2^3 \times 3 \times 5$

HCF = Product of smallest powers of common prime factors
$= 2^3 \times 3 = 24$

LCM = Product of greatest powers of all prime factors
$= 2^5 \times 3 \times 5 = 480$

Source: Chapter 1, Section 1.2 (The Fundamental Theorem of Arithmetic)

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• HCF: take the lowest power of each prime factor common to both numbers (here 2 and 3).
• LCM: take the highest power of every prime factor appearing in either number.
• Always verify: HCF × LCM = 24 × 480 = 11520 = 96 × 120 ✓
• Show the factorisation step clearly — examiners award 1 mark for correct prime factorisations and 1 mark for correct HCF and LCM values.