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SSC Sample Paper SSC CGL - Sample Paper-23

  • question_answer
    What is the LCM of \[3({{a}^{3}}-{{b}^{3}})\] and \[11({{a}^{4}}-{{b}^{4}})?\]

    A) \[33({{a}^{3}}-{{b}^{3}})({{a}^{2}}+{{b}^{2}})(a+b)\]

    B) \[({{a}^{3}}-{{b}^{3}})({{a}^{2}}+{{b}^{2}})(a-b)\]

    C) \[33(a-b)({{a}^{2}}+{{b}^{2}}-ab)({{a}^{3}}-{{b}^{3}})\]

    D) \[33({{a}^{3}}-{{b}^{3}})({{a}^{4}}-{{b}^{4}})\]

    Correct Answer: A

    Solution :

    Now, \[3({{a}^{3}}-{{b}^{3}})=3(a-b)({{a}^{2}}+{{b}^{2}}+ab)\] and \[11({{a}^{4}}-{{b}^{4}})=11(a-b)(a+b)({{a}^{2}}+{{b}^{2}})\] \[\therefore \] Required LCM \[=33({{a}^{3}}-{{b}^{3}})(a+b)({{a}^{2}}+{{b}^{2}})\]


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