Three bells beep at an interval of 12, 20, and 35 minutes. If they beep together at 10 a.m., then th

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Three bells beep at an interval of 12, 20, and 35 minutes. If they beep together at 10 a.m., then they will again beep together at

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{"content":[{"type":"paragraph","content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 1 (Identify the mathematical tool):"},{"text":" The three bells beep at intervals of 12, 20, and 35 minutes. To find when they will beep together again, we compute the Least Common Multiple (LCM) of these three intervals.","type":"text"}]},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2 (Prime Factorization of each interval):"}],"type":"paragraph"},{"content":[{"content":[{"type":"paragraph","content":[{"type":"math_inline","attrs":{"latex":"12 = 2^2 \times 3"}}]}],"type":"list_item"},{"content":[{"content":[{"attrs":{"latex":"20 = 2^2 \times 5"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"},{"content":[{"content":[{"attrs":{"latex":"35 = 5 \times 7"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"}],"type":"bullet_list"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Calculate the LCM):","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\text{LCM} = 2^2 \times 3 \times 5 \times 7 = 420 \text{ minutes}"},"type":"math_block"},{"content":[{"text":"Step 4 (Convert minutes to hours):","type":"text","marks":[{"type":"bold"}]}],"type":"paragraph"},{"attrs":{"latex":"\text{Time in hours} = \frac{420 \text{ minutes}}{60 \text{ minutes/hour}} = 7 \text{ hours}"},"type":"math_block"},{"type":"paragraph","content":[{"text":"Step 5 (Compute final time):","type":"text","marks":[{"type":"bold"}]},{"text":" The bells beeped together at 10 a.m. Adding 7 hours to this time:","type":"text"}]},{"attrs":{"latex":"10:00 \text{ a.m.} + 7 \text{ hours} = 5:00 \text{ p.m.}"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 6 (Conclusion):"},{"type":"text","text":" They will beep together again at exactly "},{"type":"text","marks":[{"type":"code"}],"text":"5:00 p.m."},{"text":".","type":"text"}],"type":"paragraph"}],"type":"doc"}

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