LCM and GCD

LCM : Least Common Multiple
GCD: Greatest Common Divisor

What is Multiple: A number multiplied by another number.
8 x 1 =   8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
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8,16,24,32,40 are multiples of 8.

What is Divisor: A number which can divide another number leaving no remainder.
 8 Divided by 2 leaves 0 as remainder.
 Therefore, 2 is Divisor.

Now lets see in detail LCM:
What is the LCM of 8 and 12.

From the example below even though 24,48,... etc are common multiples between 8 and 12. The least one among them is 24.

Therefore, LCM of 8 and 12 is 24.

8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
8 x 6 = 48

12 x 1 =12
12 x 2 = 24
12 x 3 = 36
12 x 4 = 48
12 x 5 = 60

Now lets see in detail GCD: 
What is the GCD of 8 and 12.

Divisors of 8 are 1,2,4,8. All these will leave remainder = 0.
Divisors of 12 are 1,2,3,4,6,12. All these will leave remainder = 0

Therefore, GCD of 8 and 12 is 4.