The quadratic equation x2-1088 x+295680=0 has two positive integral roots whose greatest common divisor is 16 . The least common multiple of the two roots is

Question

The quadratic equation x2-1088 x+295680=0 has two positive integral roots whose greatest common divisor is 16 . The least common multiple of the two roots is (A) 18240 (B) 18480 (C) 18960 (D) 19240

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/79786b0c3a771551a7159f23aa35cb68-.png" /> If a and b are two integers ( H ⋅ L )= ab α β=( HCF )( LCM ) 295680=16( LCM ) LCM =(295680/16)=18480

Q. The quadratic equation $x^{2} - 1088 x + 295680 = 0$ has two positive integral roots whose greatest common divisor is 16 . The least common multiple of the two roots is

18240

18480

18960

19240

If $a$ and $b$ are two integers
$(H \cdot L) = ab$
$α β = (H CF) (L CM)$
$295680 = 16 (L CM)$
$L CM = \frac{295680}{16} = 18480$

Q. The quadratic equation x2−1088x+295680=0 has two positive integral roots whose greatest common divisor is 16 . The least common multiple of the two roots is