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Exercise 38 - Example (Page 1) 		Home
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2. Find the GCF of 180, 72, and 210. (Method 2):

Find the factors:(Start with 2,3,4...)


2|180
2|90
3|45
3|15
   5

2|72
2|36
2|18
3|9
   3

 2|210
3|105
5|35
   7
Factors of 180 = 2 x 2 x 3 x 3 x 5

Factors of 72 = 2 x 2 x 2 x 3 x 3

Factors of 210 = 2 x 3 x 5 x 7

Common factors of 180, 72 and 210 are: 2 and 3

GCF = 2 x 3 = 6

3. Find the GCF of 14, 28, and 42. (Method 2):

Find the factors:(Start with 2,3,4...)


2|14
   7

 2|28
2|14
   7

 2|42
3|21
   7
Factors of 14 = 2 x 7

Factors of 28 = 2 x 2 x 7

Factors of 42 = 2 x 3 x 7

Common factors of 14, 28 and 42 are: 2 and 7

GCF = 2 x 7 = 14

4. Find the LCM of 180, 72, and 210. Factorization Method:

Find the factors:(Start with 2,3,4...)


2|180
2|90
3|45
3|15
   5

2|72
2|36
2|18
3|9
   3

 2|210
3|105
5|35
   7
Factors of 180 = 2 x 2 x 3 x 3 x 5 = 22 x 32 x 5

Factors of 72 = 2 x 2 x 2 x 3 x 3 = 23 x 32

Factors of 210 = 2 x 3 x 5 x 7

Take all the highest factors = 23 x 32 x 5 x 7 = 2520

5. Find the LCM of 180, 72, and 210. Division Method:

2|210, 180, 72
2|105, 90, 36
2|105, 45, 18
3|105, 45, 9
3|35, 15, 3
5|35, 5, 1
  7, 1, 1


L.C.M = 2 x 2 x 2 x 3 x 3 x 5 x 7 = 2520


6. G.C.F. of 12 and 20 = 4
L.C.M. of 12 and 20 = 60
Product of above G.C.F and L.C.M = 4 x 60 = 240
Product of 12 and 20 = 240
G.C.F x L.C.M of two numbers = Product of the numbers
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