How do you find the LCM for #3#, #4w+2# and #4w^2-1#?

1 Answer
George C.
Jun 8, 2015

One way is to factor each of them completely, then multiply the non-duplicated factors together. I say non-duplicated, but if a factor is repeated in one of the factorisations of the starting expressions, then it has to occur at least that many times in the LCM.

Anyway:

#3# is completely factored already.
#4w+2 = 2(2w+1)#
#4w^2-1 = (2w+1)(2w-1)#

So the unique factors are: #3#, #2#, #(2w+1)# and #(2w-1)#.

None of these factors occurs in one of the original expressions with a multiplicity greater than #1#, so we can just multiply them together to get the LCM:

#3*2*(2w+1)(2w-1) = 6*(4w^2-1) = 24w^2-6#

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