Doubt



  • F(a,b) = HCF(a,b) / LCM(a,b)
    F(1 / F(a,b) , c) = 1/12.
    a,b,c are distinct positive integers such that any pair of a,b,c are co prime to each other, then what is the sum of a, b and c ?

    Should not the answer be 11 i.e 1, 4, 6?



  • as a,b,c are coprimes to each other
    GCD(a,b) = 1 = h
    LCM(a,b)=a * b
    F(a,b) = 1/(a * b)
    now,
    F [ 1 / F(a,b) , c ] = HCF [ 1/ab,c] / LCM[1/ab,c]
    so, HCF [ 1/ab,c] = 1 / ab
    LCM [ 1/ab , c] = c
    so required function = 1/ab * 1/c = 1 / abc
    and abc = 12....given
    a = 1 , b = 3 , c = 4
    so, a + b + c = 8


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