Find the smallest number which is divisible by both 644 and 462.
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer
The smallest number divisible by both 644 and 462 is their LCM.
Prime factorisation:
$$644 = 2^2 \times 7 \times 23$$
$$462 = 2 \times 3 \times 7 \times 11$$
LCM = product of greatest powers of all prime factors:
$$\text{LCM} = 2^2 \times 3 \times 7 \times 11 \times 23 = 4 \times 3 \times 7 \times 11 \times 23 = \mathbf{21252}$$
Source: Chapter 1, Section 1.2 – The Fundamental Theorem of Arithmetic
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Explanation
- The smallest number divisible by two numbers is always their LCM — state this clearly.
- Use prime factorisation of each number, then take the highest power of every prime that appears.
- Show all working steps: factorisation → selection of highest powers → multiplication. Examiners award marks at each step, so skipping steps loses marks even if the final answer is correct.