# Least Common Multiple And Greatest Common Factor

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Name: Period: Date:Least Common Multiple and Greatest Common Factor Guide NotesMath 6Least Common Multiple (LCM)The least common multiple of two or more numbers is the least number,except 0, that is a common multiple of both (or all) of the numbers.Finding the LCM Using Listing MethodList down the multiples of each number; take note of the commonmultiples that the numbers share and choose the lowest or leastmultiple.Example: Find the LCM of 6 and 18 using listing method.Multiples of 6:6, 12, 18, 24, 30, 36, 42 Multiples of 18:18, 36, 54, 72, 90 LCM of 6 and 18 is 18.Finding the LCM Using Prime FactorizationAnother way to find the LCM of any given set of numbers is by primefactorization. This can be done using a factor tree. A factor tree is atool that breaks down the number into its prime factors.Copyright MathTeacherCoach.com1

Name: Period: Date:Least Common Multiple and Greatest Common Factor Guide NotesMath 6Example: Find the LCM of 6 and 18 using prime factorization.1. First use factor trees to find the prime factors of each number.63 1823π π π9 32ππ π π π2. Try to match the prime numbers vertically, and then bring down theprime factors in each column.6 3 218 3 3 23 3 2 18Hence, the LCM of 6 and 18 is 18.Copyright MathTeacherCoach.com2

Name: Period: Date:Least Common Multiple and Greatest Common Factor Guide NotesMath 6Sample Problem 1: Find the LCM of each set of numbers.a. 12 and 20 (by Listing Method)b. 12 and 20 (by Prime Factorization)c. 8, 10 and 40 (by Listing Method)d. 8, 10 and 40 (by Prime Factorization)Copyright MathTeacherCoach.com3

Name: Period: Date:Least Common Multiple and Greatest Common Factor Guide NotesMath 6Greatest Common Factor (GCF)The greatest common factor (GCF) of two or more numbers is thegreatest number that is a factor of all of the numbers. You can alsorefer to the greatest common factor of two or more numbers as thegreatest common divisor (GCD).Finding the Greatest Common Factor Using Listing MethodSimilar to finding the LCM of any given set of numbers, the GCF can bedetermined by the use of listing method.Example: Find the GCF of 12 and 18 using listing method.1.List down all factors of 12 and 18.Factors of 12:Factors of 18:2.1, 2, 3, 4, 6, 121, 2, 3, 6, 9, 18List the common factors that 12 and 18 share in common.Common Factors: 1, 2, 3, 63.Among the common factors, choose the greatest number. Hence,the GCF of 12 and 18 is:1, 2, 3,Copyright MathTeacherCoach.com46

Name: Period: Date:Least Common Multiple and Greatest Common Factor Guide NotesMath 6Find the GCF Using Prime FactorizationExample: Find the GCF of 12 and 18 using prime factorization.1. First use factor trees to find the prime factors of each number.181236 2239 32ππ π π πππ π π π2. Try to match the prime numbers vertically, and then bring down theprime factors that are common in all the given numbers.ππ π π πππ π π πCommon Factors:π π3. The product of the common prime factors is the GCF.Common Factors:π π πHence, the greatest common factor of 12 and 18 is 16 .Copyright MathTeacherCoach.com5

Name: Period: Date:Least Common Multiple and Greatest Common Factor Guide NotesMath 6Sample Problem 2: Find the GCF of each set of numbers.a. 15 and 20 (by Listing Method)b. 15 and 20 (by Prime Factorization)c. 24, 32 and 40 (by Listing Method)d. 24, 32 and 40 (Prime Factorization)Copyright MathTeacherCoach.com6

Name: Period: Date:Least Common Multiple and Greatest Common Factor Guide NotesMath 6Copyright MathTeacherCoach.com7

The greatest common factor (GCF) of two or more numbers is the greatest number that is a factor of all of the numbers. You can also refer to the greatest common factor of two or more numbers as the greatest common divisor (GCD). Finding the Greatest Common Factor Using Listing Method Simila

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