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  4. The LCM and the HCF of two numbers are 144 and 12 , respectively. How many such pairs of numbers are possible?

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Q. The LCM and the HCF of two numbers are 144 and 12 , respectively. How many such pairs of numbers are possible?

Number System

Solution:

Given $LCM =144$ and HCF $=12$
Let the two numbers be $x$ and $\gamma$.
$\therefore x=12 a \text { and } \gamma=12 b$
Where $a$ and $b$ are co-primes.
We have, $x \times y=$ LCM $\times$ HCF
$12 a \times 12 b=144 \times 12$
$a b=12 \Rightarrow(a, b)=(1,12)$ or $(3,4)$
There are two pairs of numbers.