Question

The HCF and LCM of two numbers are 21 and 4641, respectively. If one of the numbers lies between 200 and 300, then the two numbers are

• A. $273,363$
• B. $273,359$
• C. $273,361$
• D. $273,357$

Answer 1

The correct option is D $273,357$

Let the numbers be $21a$ and $21b$, where $a$ and $b$ are co-primes.

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

$21a\times 21b=(21\times 4641)\Rightarrow 441ab=21\times 4641\Rightarrow ab=\frac{21\times 4641}{441}\Rightarrow ab=221$

Two co-primes with product $221$ are $13$ and $17$.

Therefore, the required number is $(21\times 13,21\times 17)=(273,357)$

Hence, the two numbers are $273$ and $357$.