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
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The GCF of two numbers multiplied by their LCM will equal the product of the original numbers. If you know the GCF, divide it into the product of the two. The result will be the LCM. If the GCF of two numbers is 1, the LCM is their product.
The product of the GCF and the LCM of two numbers is equal to the product of the original two numbers. Multiply the GCF and the LCM. The original two numbers will be another factor pair of that total. Find the factor pair that has that GCF and LCM.
You need at least two numbers to find a GCF or an LCM and the LCM of those numbers can never be less than the GCF. 12 and 360 have a GCF of 12 and an LCM of 360. So do 60 and 72.
The product of the GCF and LCM of a pair of numbers is equal to the product of the numbers.
The GCF of any two prime numbers is 1 and the LCM is their product.