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Elimination Method of Finding Solution of a Pair of Linear Equations

The HCF and L...

Question

The HCF and LCM of two numbers are $33$ and $264$ respectively. When the first number is completely divided by $2$ the quotient is $33$ the other number is

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Solution

Given:
H.C.F $= 33$
L.C.M $= 264$
When the first number is completely divided by $2$ , then the quotient is $33$ and the remainder is $0$ .
Let the number be $x$
$\frac{x}{2} = 33 \Rightarrow x = 2 (33) \Rightarrow x = 66$
Let the other number be $y$ .
$H . C . F \times L . C . M = Product of two numbers \Rightarrow 33 \times 264 = x \times y \Rightarrow y = \frac{33 \times 264}{66} \Rightarrow y = 132$
Hence, the other number is $132$ ..

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