Math : LCM & GCF

Greatest Common Factor (GCF)

 The largest common factor of two or more groups. GCF is also known as Greatest common divisor ( GCD ) or Highest Common Factor (HCF )

Example 1

8 = 1 , 2 , 4 , 8
6 = 1 , 2 , 3 , 6

Here, 1,2 are the two common factors of 8 and 6. The largest is 2 hence 2 is the GCF of 8 and 6.

Example 2

10 = 1 , 2 , 5 , 10
20 = 1 , 2 , 4 , 5 , 10 , 20

Here 1,2,5,10 are the common factors of 10 and 20.
10 is the largest common factor. Hence 10 is the GCF of 10 and 20.

Least Common Multiple

 The smallest positive number that is the multiple of two or more numbers.

Example 1

3 = 3,6,9,12,15,18,21,24,27...
4 = 4,8,12,16,20,24,28...
Here 12,24... Are the common multiples of 3 and 4.
12 is the least common multiple.

Example 2

2 = 2,4,6,8,10,12,14,16..
3 = 3,6,9,12,15,18,21...
Here 6,12,18...are the common multiples of 2 and 3.
6 is the least common multiple.

Note : LCD is least common denominator.