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OpenStudy (anonymous):

I need help with gcf and lcm

OpenStudy (aroub):

post ur question! :)

OpenStudy (anonymous):

how do I find the gcf of 76

OpenStudy (aroub):

and?

OpenStudy (aroub):

i mean 76 and what?

OpenStudy (anonymous):

56

OpenStudy (anonymous):

To find the LCM of two numbers that are easy to factor I like to make a chart of the factors (and their multiplicity). \begin{array}{|c|ccc}&\\ Number &2 & 7 & 19\\ \hline 56 & 3 & 1 & 0\\ \hline 76 & 2 & 0 &1\end{array} So we have \[2^3 \cdot 7 = 8 \cdot 7 = 56\]\[2^2 \cdot 19 = 4 \cdot 19 = 76\] To find the LCM we just take the product of each of the factors raised to the max multiplicity of that factor (the biggest number in the column). \[LCM = 2^3\cdot 7^1 \cdot 19^1 = 1064 \]

OpenStudy (aroub):

if u want to find the gcf of the numbers u have 56 and 76 u write the factors of the number for 56 there is 1 and 56, 28 and 2 , 14 and 4 , 7 and 8 , okay i think this for the 56, 76= 38 and 2, 19 and 4 , 76 and 1 , okay i guess thats it now u see whats common u have 1,2,4 so 4 is the greatest so its the gcf

OpenStudy (anonymous):

You can also use the same chart I made for the LCM. The GCF is the product of the minimum values for all the columns. \[GCF = 2^2 \cdot 7^0 \cdot 19^0 = 4\]

OpenStudy (aroub):

yes..

OpenStudy (anonymous):

If it's two numbers that aren't easy to factor I have to use Euclid's method for finding the GCD, then use the equation: \[LCM(a,b) = \frac{|a\cdot b|}{GCD(a,b)}\]

OpenStudy (anonymous):

But it doesn't generalize for more than 2 numbers.

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