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

Last updated date: 21st Jul 2024
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Hint: We are given some information regarding the HCF and LCM of two numbers. For this we need to be aware about the concept of LCM and HCF. Also, we are given some information about quotients and remainder. We will use this too to calculate the numbers. We will first assume them to be equal to some variable and then apply all the information given.

Assume that the two numbers are $x$ and $y$.
We are given that when the first number is completely divided by 2, the quotient is 33. Turning this into a mathematical statement we get:
$x=2\times 33$
$\implies x=66$
Hence, the first number is 66.
Now, we move on to find the second number. We will use the following formula to find the second number:
For any two natural numbers $a$ and $b$, the following holds true:
$HCF\times LCM=x\times y$
We will plug the following values in the formula given above:
$HCF=33$
$LCM=264$
$x=66$
Putting these in the formula we get:
$33\times 264=66\times y$
$\implies y=\dfrac{264\times 33}{66}$
$\implies y=132$
Hence the other number has been found and is equal to 132.

Note: You do not actually need to apply the definitions of LCM and HCF to find the other number because that might take you a long time and it might be possible that the answer found is not correct. Using this formula will make the calculation easier and also it will give accurate results.