Algebra GCF and LCM in Laguna Beach
Algebra students in Laguna Beach often experience struggles with greatest common factor (GCF) and least common multiple (LCM).
Many times, Algebra students have understood GCF and LCM in elementary school when those problems only included numbers. But when variables are thrown into the mix in Algebra class, all understanding can go out the window.
Truthfully, finding the GCF and LCM in Algebra problems doesn’t differ much from finding the GCF and LCM in elementary math. Here are some helpful tips to remember from an Algebra.
Algebra GCF and LCM Review with Numbers
In Algebra, it helps to think about GCF and LCM in “opposite” ways. Let me explain.
When given two terms, you should first factor both terms down to their simple prime number components. So, 18 would factor to (2)(3)(3) and 20 would factor to (2)(2)(5). In order to find the GCF and LCM in Algebra, we must compare each term’s particular sets of prime numbers.
And here’s what I mean when I refer to thinking about these problems in terms of “opposites.” While the “G” in GCF stands for “greatest,” what we’ll actually do is consider the least number of all prime numbers in each term and multiply them together. So, since 18 has one factor of 2 and 20 has two factors of 2, we will only “count” one 2. Because 20 has no factors of 3 and 18 has no factors of 5, our GCF is simply 2, meaning in Algebra, 2 is the greatest number that will go into both 18 and 20.
Despite the “L” in LCM standing for “least,” to find the LCM of these two terms we actually take the greatest amount of prime numbers in each term and multiply them together. Thus, in Algebra, when we compare the 2’s, 3’s, and 5’s in both terms, we would multiply two 2’s, two 3’s, and one 5 to get 180 as our LCM. 180 is the lowest number that both 18 and 20 will eventually go into.
Algebra GCF and LCM Review with Variables
The same rules for finding the GCF and LCM in elementary math apply to finding the GCF and LCM in Algebra! Simply break down any variables with exponents to their most simplified factored state, and then consider the side with “more” and “less” using the “opposite strategy” used in elementary math.
Given the two terms 12w3y2 and 15wy4, here’s how each term would simplify:
(2)(2)(3)wwwyy and (3)(5)wyyyy
To find the GCF, we simply consider the side with the least amount of each particular number or variable, multiplying our results together. Since one term lacks a 5 and the other term lacks any 2, the only prime number we consider is 3. Between 3 w’s and 1 w, we will take the least of these and multiply 1 w. Between 2 y’s and 4 y’s, we will again take the least of these and multiply 2 y’s. Thus, the GCF of these two terms is 3wy2.
In Algebra the LCM works by finding the greater amount of a particular number or variable. So, we multiply (2)(2)(3)(5) and wwwyyyy to get 60w3y4.
As an Algebra tutor, I always suggest continue practicing GCF and LCM! If you still struggle with Algebra, try practicing your prime factorization first.