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As with every other GCF/LCM problem, your best approach MUST include a complete factorization.
y3-4y = y�(y2-4) = y�(y+2)�(y-2)
y4-8y = y�(y3-8) = y�(y-2)�(y2+2y+4)
The LCM is the collection of factors that JUST contains each factor of each element. No need to count a factor from one element if it is already included in a previous element.
Just copy the first one:
Then add whatever it does not have, that the other does.
yskip this one�(y-2)skip this one�(y2+2y+4)use this one
Gives the LCM
GCF is the collection of factors that are common to all elements.
Both have a 'y'
Both have a 'y-2'
y�(y-2) is the GCF