Question : The HCF and LCM of two numbers are 9 and 126, respectively. Find the larger number, if the ratio between the numbers is 2 : 7.
Option 1: 42
Option 2: 63
Option 3: 77
Option 4: 21
Correct Answer: 63
Solution :
Let's denote the two numbers as $2x$ and $7x$ (where $x$ is a positive integer)
The product of the two numbers is equal to the product of their HCF and LCM:
⇒ $(2x)(7x)$ = HCF $\times$ LCM
Given,
HCF = 9 and the LCM = 126
⇒ $(2x)(7x)=9\times126$
⇒ $14x^2=1134$
⇒ $x^2=81$
⇒ $x=9$
$\therefore$ Larger number = 7 × 9 = 63
Hence, the correct answer is 63.
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