LCM= Lowest Common Multiple.
GCF : To understand GCF I illustrate an example. Suppose we need to calculate the GCF of two numbers of 16 and 18 , then first we write the factors of each number as tabulated below.
Numbers

Factors


16

1

2

4

8

16


18

1

2

3

6

9

18

Therefore we can define that the factor which is the greatest one and also common among the numbers are the GCF of those numbers.In the above two rows related to 16 and 18 we notice that 1 and 2 factors are common in the two numbers. But 2 is the greatest common factor. Therefore 2 is the GCF of 16 and 18.
Let us take another example. This is tabulated below. The common factors of 36 and 48 are 1,2,3,4,and 12. But 12 is the greatest one. Therefore GCF of 36 and 48 is 12.
Numbers


36

1

2

3

4

6

12

18

36


48

1

2

3

4

6

8

12

16

24

48

LCM: To understand LCM (Lowest Common Multiple) an example is illustrated here. Suppose we need to find out the LCM of two numbers 6 and 9. First of all we multiply these numbers by 1,2,3,4,5 and so on one by one to get the multiples of these numbers. See the table below.
Numbers

multiples


6

6

12

18

24

30

36

42


9

9

18

27

36

45

54

63

Therefore the LCM of 6 and 9 is 18 because it is lowest than next common multiple i.e. 36
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