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

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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• 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.