How do you find the GCF and LCM of numbers with variables?

Answer 1

GCF is found by looking for common factors, real numbers or variables.

Find GCF for 14x2y3z and 21 xy4

factor 14x2y3z = 2.7 x x y y y z

factor 21 xy4 = 3.7 x y y y y

common factors 7, x, y, y, y 3 y's in each but only 1 x , don't use z it is not in both terms ( it is not a common factor)

multiply to get GCF 7xy3

LCM is similar in that you start by factoring, but then you must use all from each, with no repeats

Find LCM for 14x2y3z and 21 xy4

factor 14x2y3 = 2.7 x x y y y z

factor 21 xy4 = 3.7 x y y y y

factors 2, 7, x , x , y, y, y, z, 3, y now multiply all these

so LCM = 2.7 x x y y y z . 3 y = 42x2y4zthis can give us a few rules

the LCM is greater than (or equal to) the original terms

but the GCF is ledss than.

Sounds backwards, but a factor is only one part, and even the greatest part is less than the whole.

Also For LCM we use each variable with the LARGEST exponent.

for the GCF we use only common variables, and use the SMALLEST exponent.

All factors are NOT necessarily in the GCF ( notice 2, 3, and z above)

But all factors are in the LCM