Find the HCF and LCM of 72 and 120.
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
Prime factorisation:
$72 = 2^3 \times 3^2$
$120 = 2^3 \times 3 \times 5$
HCF = Product of smallest powers of common prime factors $= 2^3 \times 3^1 = **24**$
LCM = Product of greatest powers of all prime factors $= 2^3 \times 3^2 \times 5 = **360**$
Verification: HCF × LCM $= 24 \times 360 = 8640 = 72 \times 120$ ✓
Source: Chapter 1, Section 1.2 — The Fundamental Theorem of Arithmetic
---
Explanation
- What examiners look for: Write prime factorisations clearly, then state the rule for HCF (smallest powers of common factors) and LCM (greatest powers of all factors). Both values must be correct for full marks.
- The verification step (HCF × LCM = product of numbers) is a good 2-mark habit — it shows understanding and catches arithmetic errors.
- These exact numbers (72 and 120) appear as part of Example 4 in the textbook (with a third number, 6), so the factorisations are directly from the source.