Find the number of ordered pairs (a, b) such that a, b in {10, 11, …, 29, 30} and GCD(a, b) + LCM(a,

Question

Find the number of ordered pairs (a, b) such that a, b in {10, 11, …, 29, 30} and GCD(a, b) + LCM(a, b) = a + b.

Accepted Answer

{"content":[{"content":[{"text":"Step 1:","type":"text","marks":[{"type":"bold"}]},{"text":" g + l = ","type":"text"},{"type":"math_inline","attrs":{"latex":"a"}},{"text":" + b","type":"text"}],"type":"paragraph"},{"content":[{"text":"Step 2:","type":"text","marks":[{"type":"bold"}]},{"type":"text","text":" g         ab"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" g 2  (a  ","type":"text"},{"attrs":{"latex":"b"},"type":"math_inline"},{"type":"text","text":" )g  ab  0"}],"type":"paragraph"},{"type":"paragraph","content":[{"text":"Step 4:","type":"text","marks":[{"type":"bold"}]},{"text":" (g  ","type":"text"},{"attrs":{"latex":"a"},"type":"math_inline"},{"text":" )(g  ","type":"text"},{"attrs":{"latex":"b"},"type":"math_inline"},{"text":" )  0","type":"text"}]},{"content":[{"text":"Step 5:","type":"text","marks":[{"type":"bold"}]},{"text":" For ","type":"text"},{"attrs":{"latex":"a"},"type":"math_inline"},{"text":" = b, there will be 21 cases.","type":"text"}],"type":"paragraph"},{"type":"paragraph","content":[{"text":"Step 6:","type":"text","marks":[{"type":"bold"}]},{"text":" If ","type":"text"},{"attrs":{"latex":"a"},"type":"math_inline"},{"text":" = 10, ","type":"text"},{"attrs":{"latex":"b"},"type":"math_inline"},{"type":"text","text":" may be 20 or 30 as well and vice-versa."}]}],"type":"doc"}

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