6.PAR.6.2 GCF and LCM

GCF and LCM

6.PAR.6.2 Determine the greatest common factors and least common multiples using various strategies to make sense of applicable problems.

What are factors?

• Numbers that you multiply together to make a product

• Products are answers to multiplication problems.

• 3 and 5 are factors of 15 because 3 x 5 =15

• 15 is the product of the FACTORS 3 and 5.

Multiple Choice

What are all of the factors of 12?

• 1 and 12

• 1, 2, 3, 4, & 6

• 1, 2, 3, 4, 6, & 12

• 1, 2, 3, 4, 6, 10, & 12

• 12, 24, 36, 48, 72 , 84...

Greatest Common Factor (GCF)

• The greatest shared factor between two numbers.

• You can use prime factorization as a strategy to find the GCF of 2 numbers.

• The GCF of two numbers will always be the smaller of the two numbers or less

Multiple Choice

What is the Greatest Common Factor of 12 and 18?

• 1

• 3

• 6

• 8

Multiple Choice

Which pair of numbers has a GCF of 8?

• 8, 36

• 40, 80

• 16, 56

• 24, 42

What are Prime numbers?

• Whole numbers greater than 1 that only have two factors, 1 and itself

• Prime numbers are only divisible by 1 or itself

• Example: 2 is prime because the only two factors are 1 and 2, (1 x 2 = 2): 11 is prime number because the only two factors are 1 and 11 (1 x11=11).

• Can you list the first 10 prime numbers?

Multiple Select

Select all of the numbers that are prime numbers

• 15

• 7

• 9

• 2

• 13

Composite Numbers

• Whole numbers greater than 1 that are not prime numbers.

• Composite numbers have more than 2 factors.

• 4 is a composite number because it's factors are 1, 2, and 4.

​Least Common Multiple (LCM)

• ​To find the LCM you are looking for the smallest common skip number

• ​You typically look for the key words: same time

• ​Example: LCM of 8 and 5

• ​8: 8, 16, 24, 32, 40, 48

• ​5: 5, 10, 15, 20, 25, 30, 35, 40​

• ​LCM = 40

Multiple Choice

multiples for the number 3 include..

• 4,8,12,16,18,21
• 3,5,7,9,10,12
• 3,4,5,6,7,8
• 3,6,9,12,15,18

Multiple Choice

Find the LCM of 4 and 9

• 4

• 9

• 13

• 36

Prime Factorization

• Can be used to find the GCF and LCM of two numbers.

• Find all of the prime factors of a given number

• There is only one prime factorization of any number.

To find the prime factorization:

1. Divide the number by the first prime number possible.

2. Circle the prime number, and continue with the other factor.

3. Divide the new factor by a prime number.

4. Continue this process until the only numbers you have left are prime numbers.

15 is a composite number.

It can be written as a product of primes: 3 x 5

Some text here about the topic of discussion

​Example

Multiple Choice

What is the missing factor?

4 x _____ = 28

• 12

• 6

• 7

• 9

Multiple Choice

Use a number tree to find the prime factorization of 60

• 5 x 3 x 2 x 2

• 7 x 6 x 5

Multiple Choice

Use a number tree to find the prime factorization of 42

• 4 x 4 x 3

• 7 x 3 x 2

Distributive Property:  Multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting. (Rainbow Connection!)

Example:  6(2+4)= 6(2) + 6(4)     8(5-3) = 8(5)-8(3)

Fill in the Blank

Write an equivalent expression for 18 + 27 by factoring out the GCF.