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# How do you find the Gcf of $12$ and $18$?

Last updated date: 05th Mar 2024
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Hint: In the given question, we have been given to calculate the HCF of two numbers. For finding the HCF, we use the relation between LCM, HCF, and the product of two numbers. This gives us the HCF or the GCD of the two numbers.

Formula Used:
We are going to use the relation between LCM, HCF, and the product of two numbers.
$LCM\left( {a,b} \right) \times HCF\left( {a,b} \right) = a \times b$

Complete step by step solution:
The given two numbers are $12$ and $18$.
To find the HCF, we calculate the LCM.
$\begin{array}{l}2\left| \!{\overline {\, {12,18} \,}} \right. \\2\left| \!{\overline {\, {6,9} \,}} \right. \\3\left| \!{\overline {\, {3,9} \,}} \right. \\3\left| \!{\overline {\, {1,3} \,}} \right. \\{\rm{ }}\left| \!{\overline {\, {1,1} \,}} \right. \end{array}$
Hence, the LCM is $2 \times 2 \times 3 \times 3 = 36$
Now, we divide the product of the numbers by their LCM to find their HCF,
$HCF = \dfrac{{12 \times 18}}{{36}} = 6$

Hence, the HCF of the two numbers is $6$.