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. $78$
• B. $91$
• C. $104$
• D. $117$

Answer 1

The correct option is B $91$

Let the numbers be $13a$ and $13b$, where $a$ and $b$ are co-primes.

We know that LCM$\times$HCF=Product of two numbers, therefore, we have,

$13a\times 13b=13\times 455\Rightarrow 169ab=5915\Rightarrow ab=\frac{5915}{169}\Rightarrow ab=35$

Two co-primes with product $35$ are $5$ and $7$.

Therefore, the required number is $(13\times 5,13\times 7)=(65,91)$

Hence, the number that lies between $75$ and $125$ is $91$.