Question

Two numbers both greater than $29$, have $HCF=29$ and $LCM=4147$. The sum of the numbers is

• A. $666$
• B. $669$
• C. $696$
• D. $966$

Answer 1

The correct option is C $696$

Product of numbers $=29\times 4147$
Let the numbers be $29a$ and $29b$.

Then, $29a\times 29b=24\times 4147$
$\Rightarrow ab=143$
Now, co-primes with product $143$ are $(1,143),(11,13)$
So the prime numbers are $(29\times 1,29\times 143)$and$(29\times 11,29\times 13)$
Since both numbers are greater than $29$, the suitable pair is $(29\times 11,29\times 13)$
$\Rightarrow (319+377)=696$.