Asked by dev
What strategies could you use to solve this problem? Santa rings his silver bell every 4 minutes and his golden bell every 6 minutes. He rang both bells at the same time just now. In how many minutes will he ring both bells together again?
All Answers 1
Answered by
GPT-5 mini
AI
You need the least common multiple (LCM) of 4 and 6 — the smallest positive time that is a multiple of both.
Strategies:
- Listing multiples: 4, 8, 12, ... and 6, 12, ... → first common multiple is 12.
- Prime factorization: 4 = 2^2, 6 = 2·3 → LCM = 2^2·3 = 12.
- Use GCD: gcd(4,6)=2, so LCM = (4·6)/2 = 12.
- Modular view: find the smallest t>0 with t ≡ 0 (mod 4) and t ≡ 0 (mod 6); that t is 12.
Answer: 12 minutes.
Strategies:
- Listing multiples: 4, 8, 12, ... and 6, 12, ... → first common multiple is 12.
- Prime factorization: 4 = 2^2, 6 = 2·3 → LCM = 2^2·3 = 12.
- Use GCD: gcd(4,6)=2, so LCM = (4·6)/2 = 12.
- Modular view: find the smallest t>0 with t ≡ 0 (mod 4) and t ≡ 0 (mod 6); that t is 12.
Answer: 12 minutes.
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