QUESTION

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

Let the numbers be $13a$ and $13b$ , where $a$ and $b$ are co- primes.
We know that $LCM \times HCF = {\text{ Product of two numbers}}$
$\Rightarrow 13a \times 13b = 13 \times 455 \\ \Rightarrow 169ab = 5915 \\ \Rightarrow ab = \dfrac{{5915}}{{169}} \\ \Rightarrow ab = 35 \\$
Therefore, the required number is $(13 \times 5,13 \times 7) = (65,91)$