# What is the Least Common Multiple | Find LCM | Easy way to find LCM

This topic is our LCM, we will learn about  Multiples, Multiplier, What is the Least Common Multiple,  Division method, Easy way to find LCM of large numbers etc, and  LCM further and will do some questions related to it and if we learn some short tricks also, let us start. LCM First we need to know Multiples and Multiplier

## Multiples

The qualitative form of a number is called its multiples.
Example :    Multiples of 25 = 50 , 75, 100............

## Multiplier

All the numbers which are divisible by a number are called multiplier of that number.
Example :     Multiplier of  32  =  1, 2, 4, 8, 16, 32

## What is the Least Common Multiple

The smallest value of the order of any given number, which is completely divisible by all the numbers of the whole series, is called the least common multiple.
Example:  L.c.m 60 of 4,5,6 ## How to find the least common multiple

There are two ways to get l.c.m.

### (a) Multiplication method

Factor method is that in which we find the LCM of numbers. To extract l.c.m of numbers, first we write them respectively as their prime factors.
Example: 8, 18
8 = 2 x 2 x 2
18 = 2 x 3 x 3
Then we find the common in it, then write it down and write the rest of the number as the product respectively, after the product we get the result is the l.c.m of both the numbers.
2 x 2 x 2 x 3 x 3
Just like two is our common, so we will write 2 once.
2 x 2 x 2 x 3 x 3 = 72
Now we know that l.c.m of 8 and 18 is 72.
Similarly you can extract l.c.m of more numbers

### (b) Division method

To find the LCM by division method we can divide by the smallest number except one. We have to give the division by the same small number which is divided by at least two numbers. Write the quotient of the numbers which are divisible by that number and the numbers which do not divide will be written in the same form. Do the same action until the bottom stops dividing by two numbers or one number. Either all the numbers below become one.
2 | 34,44
⎺⎺⎺⎺⎺⎺⎺⎺⎺⎺
2  | 17, 22
⎺⎺⎺⎺⎺⎺⎺⎺⎺⎺
|  17, 11
⎺⎺⎺⎺⎺⎺⎺⎺⎺⎺
2 x 2 x 17 x 11 = 748

## Easy way to find LCM of large numbers

Trick number 1. To remove LCM. if you are given a number. So choose the largest number from that number if it is divided by the rest of the numbers. So the same number will be its lcm.
Let's solve a question on this short trick.
If the given number is something like this. Find the lcm of 9, 27, 54.
So according to this trick
The highest number in the given question is 54.
then
54/9 = 6 , 54/27 = 2
Therefore 54 will be its lcm.

Trick number 2. If a number is in the form of ambush and their base is the same, then the number that has the most ambush (power) is the LCM. it happens.

Let's solve a question on this short trick.
Given number 9 ambush (power) 1, 9 ambush (power) 3, 9 ambush (power) 4, 9 ambush (power) 5,
then  9 has the highest power at 5
So according to this trick
9 x 9 x 9 x 9 x 9 = 59049
Trick number 3. If you are given a number and need to remove its lcm, write the given number as the power of the product of the prime numbers. Then the product of the factors with the greatest power of prime numbers will be its lcm.
If the given number is something like this.
1. Find the lcm of  25, 27, 16 .
Let's solve a question on this short trick.
The numbers we have to find LCM. Let's write it as ambush first.
25 =  5 to the power of 5
27 =  3 to the power of 3
16 =  4 to the power of 4