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  4. The LCM and the HCF of two numbers are 1001 and 7 , respectively. How many such pairs are possible?

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Q. The LCM and the HCF of two numbers are 1001 and 7 , respectively. How many such pairs are possible?

Number System

Solution:

Given $LCM =1001$ and $HCF =7$
Let the two numbers be $x$ and $\gamma$.
$\therefore x=7 a$ and $y=7 b$, where $a$ and $b$ are co-primes.
We have, $x \times y= LCM \times HCF$ $7 a \times 7 b=1001 \times 7$ $a b=143 \Rightarrow(a, b)=(1,143)$ or $(11,13)$ $\Rightarrow$ There are two pairs of numbers.