The HCF and LCM of two number are 13 and 455 respectively. If one of the number is lies between 75 and 125, then that number is :

The HCF and LCM of two number are 13 and 455 respectively. If one of the number is lies between 75 and 125, then that number is :
[A]78
[B]91
[C]104
[D]117

91
HCF = 13
Let the numbers be 13x and 13y, where x and y are co-prime to each other.
∴ LCM = 13xy
∴ 13xy = 455
\therefore xy = \frac{455}{13} = 35 = 5\times 7
∴ Numbers are 13 \times 5 = 65 and 13 \times 7 = 91
Hence option [B] is correct answer.

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