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LESSON 1-1
Greatest Common Factor
Vocabulary
Common factor: A whole number that is factor of two or more nonzero
whole numbers is a common factor of the numbers
Greatest Common Factor (GCF): The greatest common factor is the largest of the common factors.
Method 1
List all the factors of 96 and 180…
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The common factors are 1, 2, 3, 4, 6, and 12
The GCF is 12
--------------------------------------------------------------------------------------------------3 Numbers…
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The common factors are 1, 2, 3, and 6
GCF:
6
Least Common Multiple
Vocabulary
Multiple:
A multiple of a number is the product of the number and any nonzero
whole number
Common multiple:
A multiple shared by two or more numbers is a common
multiple.
Least Common Multiple (LCM):
The least common multiple of two or more
numbers is the smallest of the common multiples.
Finding the Least Common Multiple (LCM)
The least common multiple of two or more numbers is the smallest of the common
multiples . Below are two methods to find the LCM.
Method 1 Start listing the multiples of each number. Then find the smallest of the
common multiples .
Method 2 Write the prime factorization of the numbers. Multiply together the
prime factors . Use each prime factors the greatest number of times of times it is a
factor of any of the numbers.
METHOD 1
Using Multiples
Find the LCM of 6 and 16.
Multiples of 6:
6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 ,…
Multiples of 16:
16 , 32 , 48 , 64 , 80 , 96 ,…
Answer: The LCM of 6 and 16 is 48
.
METHOD 2
Using Prime Factorization
Find the LCM of 30 and 36 using prime factorization.
1. Write the prime factorizations. Circle any common factors.
30 =
36 =
2.
Multiply together the prime factors using each circled factor the greatest
number of times it occurs.
2  2  3  3  5 = 180 .
Answer: The LCM of 30 and 36 is 180 .