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    If the LCM of 20x3y220x^3y^220x3y2 and 10x4y410x^4y^410x4y4 is 20x4y420x^4y^420x4y4 , find the HCF.​
    Question

    If the LCM of 20x3y220x^3y^2 and 10x4y410x^4y^4 is 20x4y420x^4y^4 , find the HCF.​

    A.

    10x2y210x^2y^2​​

    B.

    20x2y220x^2y^2​​

    C.

    20x3y220x^3y^2​​

    D.

    10x3y210x^3y^2​​

    Correct option is D

    Given:

    We are given the two expressions:

    20x3y220x^3y^2 ,  10x4y410x^4y^4​ 

    and their least common multiple (LCM) = 20x4y420x^4y^420x4y420x^4y^4

    Formula Used:

     LCM × HCF = Product of the numbers

    Solution:

    We substitute the values into the formula ;LCM×HCF=Product of the numbers\text{LCM} \times \text{HCF} = \text{Product of the numbers}

    (20x4y420x^4y^420x4y420x^4y^4)×HCF =  (20x3y220x^3y^2)×(10x4y410x^4y^4 )

    HCF=20x3y2×10x4y420x4y4\text{HCF} = \frac{20x^3y^2 \times 10x^4y^4}{20x^4y^4}

    HCF=10x3y2\text{HCF} = 10x^3y^2  

    The HCF  of  20x3y220x^3y^2 and 10x4y410x^4y^4 = 10x3y210x^3y^2​​

    10x4y410x^4y^4



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