University:
California State University, Northridge
Course:
MATH 102 | Pre-Calculus I
Academic year:

2024
Views:

250

Pages:

3
Author:

Lorelai Pope

The procedure for finding the GCF is as follows: 1. Find the prime factorization of each number 2. Identify COMMON primes. 3. Pull the common primes with the least power. 4. The product of step 3 is the GCF . Go over the examples in the module . You will be finding GCF's and LCM's from now through the end of the semester . Example: The following is an example that uses the tree method . ........................................... From the tree we see that the prime factorization of 1248 = and 420 = . GCF = (The primes common to both numbers are 2 and 3 . But 2 is not the GCF! We need to take the least exponent attached to a 2 , in this case is the GCF of 1248 and 420.) that means 2 . Thus Note: With two numbers as large as 420 and 1248 is may seem strange that the biggest number that divides evenly into both numbers is 4.But what about 1248 and 1249 ? The biggest number that divides evenly into both of these numbers is 1 ! The procedure for finding the LCM is as follows: 1. Find the prime factorization of each number (use prime factor tree method ) 2. List ALL primes used in either of the numbers . 3. Attach the highest exponents belonging to each given prime . 4. The product of these primes with highest exponents is the LCM. Example: To find the LCM of 1248 and 420 find the prime factors as follows : ... Thus the prime factorization of 1248 = and 420 = LCM = (Following the procedure to step 2 we take ALL primes in each factorization and list them : 2 , 3 , 5 , 7 , 13 . These are the different numbers that were circled above. Now we take the highest exponent belonging to each prime . The highest exponent belong to 2 is 5 . The highest exponent belonging to 3, 5, 7, and 13 is 1 ( a number with no exponent actually has the "implied" exponent 1). Hence the LCM of 1248 and 420 is . Practice Problem: #1 Find the GCF of {72, 630, 378} #2 Find the LCM of {72, 630, 378} Solution #1 Find the prime factorization of {72, 630, 378}first: 72 = 630 = 378 = Common prime are 2 and 3. The least exponent attached to 2 is 1 and the least exponent attached to 3 is 2. Therefore, GCF = = = 18. #2 List ALL prime from above: 2, 3, 5, 7, then take the highest exponent attached to each prime, which is 3, 2, 1 and 1 respectively. Therefore, LCM = .