### Definition Of LCM No-1

The least common denominator is the smallest number that is completely divisible by the given numbers. Which is the definition of LCM (least common denominator)

**Example**

** **

For example, the least common multiple of 6, 8,12 is 24.This means that 24 is the smallest

number that is divisible by 6 8 12.

### Definition Of LCM No-2

The least common denominator is the product of the smallest expressions. Which is completely divided by the given expressions.

**Example**

** **

If the least common multiple of x2, x3, x4 is x5. So this means that x5 is the smallest expression which is completely divided by x2, x3, x4.

### Definition Of LCM No-3

The smallest product of a number by two or by two which is completely divided by those numbers.

**Example**

The least common multiple of 3,612?

Table of 3 = 3, 4, 6, *12*, 15, 14, 21, 26, 24,30.

Table of 6 = 6, *12* 18, 24, 30, 36, 42, 48, 60.

Table of 12 = *12*, 24,36, 48, 60, 72, 84, 96,108, 120.

We see that only 12 common are being found in all three numbers. We can say that the number is the least common multiple of 3,6, 12.

**Note – **If the common number is two or more, then the smallest common number will be considered as the least common denominator.

### Definition Of LCM No-4

We can understand the least common denominator in this context. Suppose there are three ball A, B, C. Whose diameters are 2, 9, 12. Which has two holes E and F (Size 12, 26). If the n ball is inserted into the hole, all three balls will be easily crossed. But we can call the smallest hole as the least common denominator.

### Definition Of LCM No-5 With Help Of Venn Diagram

The above diagram shows two Venn diagrams. There is 24 in the middle of one and 4 in the middle of the other. And around them are 2, 4, 4, 7 which divide both the middle numbers. 24 is the smallest number. Which is divided by numbers 2, 4, 6, 4. This means that there cannot be a number smaller than 24 which can be divided by numbers 2, 4, 6, 7.