Gcf&Lcm
-
Upload
kate-rimando -
Category
Documents
-
view
1.031 -
download
1
Transcript of Gcf&Lcm
![Page 1: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/1.jpg)
PRIME FACTORIZATIONGCF & LCM
![Page 2: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/2.jpg)
FACTORING
Factoring is the opposite of multiplying A Factor Times another Factor Equals a Product A Composite Number can be factored by two or more numbers Factoring is breaking Down a Product into it’s Factors Prime Factorization is breaking down a Product into it’s Prime Factors.
![Page 3: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/3.jpg)
FACTOR TREE
A factor tree breaks a product down into it’s Prime Factors. It is called PRIME FACTORIZATION
30
3 10
3 • 2 • 5
PRODUCT
PRIME FACTORS
![Page 4: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/4.jpg)
Prime Factorization
Factor 225
![Page 5: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/5.jpg)
Prime Factorization
Factor 225
1. Put number on top of factor tree. 225
![Page 6: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/6.jpg)
Prime Factorization
Factor 225
1. Put number on top of factor tree.
2. Find factors and branch down tree
225
5 45
5 9
5 • 5 • 3 • 3 = 32 • 52
![Page 7: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/7.jpg)
GCF - Greatest Common Factor
The GCF of two numbers is the greatest number that divides into both numbers evenly.
Ex: The GCF of 14 & 35 is 7, since 7 is the greatest number that goes into both 14 & 35 evenly
![Page 8: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/8.jpg)
HOW TO FIND THE GCF
The key to determining the GCF is to identify Common Factors in Both Numbers and Multiplying them together.
![Page 9: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/9.jpg)
COMMON FACTORS OF 225 & 30
THE COMMON FACTORS ARE 5 & 3
225
5 45
5 9
5 • 5 • 3 • 3
3 10
30
3 • 5 • 2
![Page 10: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/10.jpg)
IDENTIFY COMMON FACTORS
3 • 5 • 2 7 • 5 • 2 • 17
![Page 11: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/11.jpg)
IDENTIFY COMMON FACTORS
THE COMMON FACTORS ARE 5 & 2
3 • 5 • 2 7 • 5 • 2 • 17
![Page 12: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/12.jpg)
IDENTIFY COMMON FACTORS
7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7
![Page 13: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/13.jpg)
IDENTIFY COMMON FACTORS
THE COMMON FACTORS ARE 7 & 5 & 5
7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7
![Page 14: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/14.jpg)
IDENTIFY COMMON FACTORS
7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7&
2 • 11 • 5 • 3 • 7 13 • 3 • 2 • 5 • 2&
3 • 5 • 11 • 3 • 3 2 • 2 • 2 • 17 • 7&
5 • 5 • 7 • 3 2 • 5 • 2 • 3& 2 • 5 • 2 • 7&
For three numbers common factors must be in all three numbers
![Page 15: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/15.jpg)
IDENTIFY COMMON FACTORS
7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7&
2 • 11 • 5 • 3 • 7 13 • 3 • 2 • 5 • 2&
3 • 5 • 11 • 3 • 3 2 • 2 • 2 • 17 • 7&
5 • 5 • 7 • 3 2 • 5 • 2 • 3& 2 • 5 • 2 • 7&
For three numbers common factors must be in all three numbers
5•5•7
2•5•3
None
Only 2 is in common
![Page 16: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/16.jpg)
Finding Greatest Common FactorFind GCF of 225 & 30
![Page 17: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/17.jpg)
Finding Greatest Common Factor
225
5 45
5 9
5 • 5 • 3 • 3
3 10
30
3 • 5 • 2
Find GCF of 225 & 30
1. Complete Factor Tree for both numbers.
![Page 18: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/18.jpg)
Finding Greatest Common Factor
THE COMMON FACTORS ARE 5 & 3
225
5 45
5 9
5 • 5 • 3 • 3
3 10
30
3 • 5 • 2
Find GCF of 225 & 30
1. Complete Factor Tree for both numbers.
2. Identify Common Factors.
![Page 19: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/19.jpg)
Finding Greatest Common Factor
THE COMMON FACTORS ARE 5 & 3
225
5 45
5 9
5 • 5 • 3 • 3
3 10
30
3 • 5 • 2
Find GCF of 225 & 30
1. Complete Factor Tree for both numbers.
2. Identify Common Factors.
3. Multiply Common Factors for GCF
GCF = 5 • 3 = 15
![Page 20: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/20.jpg)
Finding the LCMLeast Common Multiple
The LCM is the Lowest Number that is a Multiple of Both Numbers.Ex. The LCM of 12 & 9 is 36 since both 12 & 9 divide evenly into 36.
Hint: Think of Common Denominators in Fractions.A common denominator is the LCM of the denominators.
€
1
6+
1
8=
4
24+
3
24=
7
24
![Page 21: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/21.jpg)
Finding the LCMLeast Common Multiple
![Page 22: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/22.jpg)
Finding Least Common MultipleFind LCM of 45 & 25
![Page 23: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/23.jpg)
Finding Least Common Multiple
45
5 9
5 • 3 • 3 5 • 5 • 3
25 3
Find LCM of 45 & 25
1. Complete Factor Tree for both numbers.
75
![Page 24: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/24.jpg)
Finding Least Common Multiple
THE COMMON FACTORS ARE 5 & 3
45
5 9
5 • 3 • 3 5 • 5 • 3
25 3
Find LCM of 45 & 25
1. Complete Factor Tree for both numbers.
2. Identify Common Factors.
75
![Page 25: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/25.jpg)
Finding Least Common Multiple
THE COMMON FACTORS ARE 5 & 3
45
5 9
5 • 3 • 3 5 • 5 • 3
25 3
Find LCM of 45 & 25
1. Complete Factor Tree for both numbers.
2. Identify Common Factors.
3. Multiply Common Factors with ALL OTHER FACTORS
LCM = CF’s•ALL OTHER FACTORSLCM = 5•3 • 5 • 3 = 225
75
OTHER FACTORS
![Page 26: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/26.jpg)
Finding Least Common MultipleFind LCM of 12 & 34
1. Complete Factor Tree for both numbers.
2. Identify Common Factors.
3. Multiply CF’s with ALL OTHER FACTORS
![Page 27: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/27.jpg)
Find LCM of 225, 10 & 66
Finding the LCMLeast Common Multiple
(FOR 3 NUMBERS)
![Page 28: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/28.jpg)
Find LCM of 225, 10 & 66
1. Complete Factor Tree for all numbers.
Finding the LCMLeast Common Multiple
(FOR 3 NUMBERS)225
5 45
5 9
5 • 5 • 3 • 3
11 6
66
11 • 3 • 2
5 • 2
10
![Page 29: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/29.jpg)
Find LCM of 225, 10 & 66
1. Complete Factor Tree for all numbers.
2. Identify Common Factors OF ANY 2 #’S.
Finding the LCMLeast Common Multiple
(FOR 3 NUMBERS)
THE COMMON FACTORS ARE 2,5 & 3
225
5 45
5 9
5 • 5 • 3 • 3
11 6
66
11 • 3 • 2
5 • 2
10
![Page 30: Gcf&Lcm](https://reader036.fdocuments.in/reader036/viewer/2022070316/555e6c16d8b42a34098b4d30/html5/thumbnails/30.jpg)
Find LCM of 225, 10 & 66
1. Complete Factor Tree for all numbers.
2. Identify Common Factors OF ANY 2 #’S.
3. Multiply Common Factors with ALL OTHER FACTORS
OTHER FACTORS
Finding the LCMLeast Common Multiple
(FOR 3 NUMBERS)
THE COMMON FACTORS ARE 2,5 & 3
225
5 45
5 9
5 • 5 • 3 • 3
11 6
66
11 • 3 • 2
5 • 2
10
LCM=2•5•3•5•3•11=4950