The ABC’s of GCF and LCM

GCF = Greatest Common Factor If the word factor is in the name, I know this has to do with multiplication. Greatest obviously means the factor with the largest value Common must mean more than one number has this single factor

Greatest Common Factor The Greatest Common Factor is the largest factor two or more numbers share How do you find the GCF of 12 and 18? Using the rules of divisibility, find all of the factors of 12 and 18 12= 1, 2, 3, 4, 6, 12 18 = 1, 2, 3, 6, 9, 18

Greatest Common Factor 12= 1, 2, 3, 4, 6, 12 18 = 1, 2, 3, 6, 9, 18 Find the numbers that occur in both lists Choose the number that is the largest The Greatest Common Factor of 12 and 18 is 6

Greatest Common Factor Find the GCF between 75 and 30 Use the rules of divisibility to help you 75 –ends in 5 5 * 15 - digits add to 12 (which is divisible by 3) 3 * 25 - follows the identity property 1* 75 The factors of 75 are 1, 3, 5, 15, 25, 75

Greatest Common Factor Find the GCF between 75 and 30 Use the rules of divisibility to help you 30 –ends in 5 and 0 5 * 6 3 * 10 - is an even number 2 * 15 - follows the identity property 1* 30 The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

Greatest Common Factor Compare the two strings of factors and find the largest common factor: 75 = 1, 3, 5, 15, 25, 75 30 = 1, 2, 3, 5, 6, 10, 15, 30 The Greatest Common Factor is 15

Greatest Common Factor and Factor Trees Create factor trees for 18 and 30- remember to divide down to the prime factorization of each number 18 30 3 * 6 5 * 6 3 * 2 3*2 3*3*2 5 * 3 * 2

Greatest Common Factor and Factor Trees 18 30 3 * 6 5 * 6 3 * 2 3*2 3*3*2 5 * 3 * 2 3 and 2 are common in both prime factorization, therefore 3*2 or 6 is the GCF

Practice Time Math Journal 2 page3 405-407 Math Practice Book 13.2

Least Common Multiple If the word multiple is in the name, I know this has to do with multiplication A multiple is the product of two numbers that are multiplied together 7*3 = 21 21 is the multiple of 7 and 3 Least means I am looking for the smallest multiple Common means the multiple must be included in both numbers multiple strings

Least Common Multiple Find the Least Common Multiple of 4 and 6 List the multiples in order for each number: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48… 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72… What is the smallest number that sits in both strings?

Least Common Multiple Find the Least Common Multiple of 4 and 6 List the multiples in order for each number: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48… 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72… What is the smallest number that sits in both strings?

6 and 8 3 and 8 6 and 9 24 24 18 Least Common Multiple Find the LCM of: 6 and 8 3 and 8 6 and 9 24 24 18

Practice LCM Math Practice Book 13.3

Using Factor Trees to find the LCM Use factor trees to find the prime factorization for 18 and 30 18 30 3 * 6 5 * 6 3 * 2 3*2 3*3*2 5 * 3 * 2 3*2 repeats in both factor strings

Using Factor Trees to find the LCM 3*3*2 3 * 2 * 5 3*2 repeats in both factor strings Eliminate one set of 3 * 2 and multiply the rest of the prime factors together 3 * 3 * 2 * 5 90 The LCM of 18 and 30 is 90

Greatest Common Factor and Factor Trees 18 30 3 * 6 5 * 6 3 * 2 3*2 3*3*2 5 * 3 * 2 3 and 2 are common in both prime factorization, therefore 3*2 or 6 is the GCF

Factoring out the LCM Find the LCM using factor tree method for: 12 and 42 32 and 20 16 and 24 84 160 48

Factoring out the LCM Practice this method Math Journal 2 page 408