What is the least positive integer that is exactly divisible by all the integers from 1 to 10?

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{"content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (LCM Concept):","type":"text"},{"text":" The least positive integer divisible by all numbers from 1 to 10 is the Least Common Multiple (LCM) of the set ","type":"text"},{"attrs":{"latex":"\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}"},"type":"math_inline"},{"text":".","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Calculate the LCM):","type":"text"},{"type":"text","text":" We factor each number and take the highest power of each prime:"}],"type":"paragraph"},{"content":[{"type":"list_item","content":[{"content":[{"text":"Prime 2: highest power is ","type":"text"},{"attrs":{"latex":"2^3 = 8"},"type":"math_inline"},{"type":"text","text":" (from 8)"}],"type":"paragraph"}]},{"content":[{"content":[{"text":"Prime 3: highest power is ","type":"text"},{"attrs":{"latex":"3^2 = 9"},"type":"math_inline"},{"text":" (from 9)","type":"text"}],"type":"paragraph"}],"type":"list_item"},{"content":[{"content":[{"text":"Prime 5: highest power is ","type":"text"},{"attrs":{"latex":"5^1 = 5"},"type":"math_inline"},{"text":" (from 5, 10)","type":"text"}],"type":"paragraph"}],"type":"list_item"},{"type":"list_item","content":[{"content":[{"text":"Prime 7: highest power is ","type":"text"},{"attrs":{"latex":"7^1 = 7"},"type":"math_inline"},{"text":" (from 7)","type":"text"}],"type":"paragraph"}]}],"type":"bullet_list"},{"attrs":{"latex":"\text{LCM} = 2^3 \times 3^2 \times 5^1 \times 7^1 = 8 \times 9 \times 5 \times 7 = 2520"},"type":"math_block"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"text":" The least positive integer is 2520, which is at option index ","type":"text"},{"marks":[{"type":"code"}],"text":"1","type":"text"},{"text":" in the options ","type":"text"},{"marks":[{"type":"code"}],"text":"['1260', '2520', '5040', '720']","type":"text"},{"text":".","type":"text"}]}],"type":"doc"}

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