9/26/2019

Definition Of LCM (Least common multiple) With Full Explanation And Example

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 least common multiple

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 least common multiple

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.
Definition Of LCM We can understand the least common denominator in this context


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