Find the least common multiple of 21, 35 and 49 using prime factorisation.
Answer
735
The correct answer is 735 — Therefore the LCM of 21, 35 and 49 is 735.
Step-by-step solution
- Prime‑factorise each number: - 21 = 3 × 7 - 35 = 5 × 7 - 49 = 7 × 7.
- For each prime, take the highest power that occurs: - 3^1 (from 21) - 5^1 (from 35) - 7^2 (from 49).
- Multiply these highest powers: 3 × 5 × 7^2 = 3 × 5 × 49 = 735.
- Therefore the LCM of 21, 35 and 49 is 735.
Common mistake: Failing to take the highest power of a common prime
Concept tested: LCM by prime factorisation
Published · How this solution was prepared and checked
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