Three bells ring at intervals of 6, 12 and 18 minutes. If all the three bells rang at 6 a.m., when will they ring together again?
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
The three bells will ring together again after LCM(6, 12, 18) minutes.
Prime factorisation:
- $6 = 2 \times 3$
- $12 = 2^2 \times 3$
- $18 = 2 \times 3^2$
LCM = $2^2 \times 3^2 = 4 \times 9 = \mathbf{36}$ minutes
Since all three bells rang together at 6:00 a.m., they will ring together again at 6:36 a.m.
Source: Chapter 1, Section 1.2 – The Fundamental Theorem of Arithmetic
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Explanation
- The key concept: bells ringing at regular intervals will next ring together at the LCM of those intervals.
- Use prime factorisation to find LCM — take the greatest power of each prime factor appearing in any of the numbers.
- Don't forget the final step: add 36 minutes to 6:00 a.m. to state the actual time. Examiners expect this conclusion, not just the LCM value.
- This is a standard application question from Exercise 1.1 type problems in Chapter 1.