The LCM of two numbers is 7200, and their HCF is 180. If one number is 360, then the second number i

Question

The LCM of two numbers is 7200, and their HCF is 180. If one number is 360, then the second number is ________.

Accepted Answer

{"content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (State the Theorem):","type":"text"},{"text":" For any two positive integers ","type":"text"},{"attrs":{"latex":"a"},"type":"math_inline"},{"text":" and ","type":"text"},{"type":"math_inline","attrs":{"latex":"b"}},{"text":", the product of the two numbers is equal to the product of their Least Common Multiple (LCM) and Greatest Common Divisor / Highest Common Factor (HCF):","type":"text"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"a \times b = \text{LCM}(a, b) \times \text{HCF}(a, b)"}},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Substitute the Values):","type":"text"},{"text":" We are given:","type":"text"}],"type":"paragraph"},{"content":[{"content":[{"content":[{"attrs":{"latex":"\text{LCM} = 7200"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"},{"content":[{"content":[{"attrs":{"latex":"\text{HCF} = 180"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"},{"type":"list_item","content":[{"content":[{"type":"text","text":"One number "},{"attrs":{"latex":"a = 360"},"type":"math_inline"}],"type":"paragraph"}]}],"type":"bullet_list"},{"type":"paragraph","content":[{"text":"Let the second number be ","type":"text"},{"attrs":{"latex":"b"},"type":"math_inline"},{"type":"text","text":". Substituting these values:"}]},{"attrs":{"latex":"360 \times b = 7200 \times 180"},"type":"math_block"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Solve for the Second Number b):","type":"text"}]},{"attrs":{"latex":"b = \frac{7200 \times 180}{360}"},"type":"math_block"},{"type":"math_block","attrs":{"latex":"b = 7200 \times \frac{180}{360} = 7200 \times 0.5 = 3600"}},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 4 (Conclusion):"},{"type":"text","text":" The second number is exactly "},{"marks":[{"type":"code"}],"text":"3600","type":"text"},{"text":".","type":"text"}],"type":"paragraph"}],"type":"doc"}

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