Question

HCF and LCM of two numbers are $7$ and $140$, respectively. If the numbers are between $20$ and $45$, then what is the sum of the numbers?

• A. $43$
• B. $53$
• C. $63$
• D. $73$

Answer 1

The correct option is C $63$

Let the numbers be $7a$ and $7b$, where $a$ and $b$ are co-primes.

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

$7a\times 7b=(7\times 140)\Rightarrow 49ab=7\times 140\Rightarrow ab=\frac{7\times 140}{49}\Rightarrow ab=20$

Two co-primes with product $20$ are $4$ and $5$.

Therefore, the required number is $(7\times 4,7\times 5)=(28,35)$

The sum of these numbers is $28+35=63$

Hence, the sum of the numbers is $63$.