How to Find LCM

In this article, you will learn about how to find LCM of two or more than two numbers. But before understanding the formula or method to calculate LCM of given numbers. Let's first understand about LCM.

What is LCM ?

LCM stands for Least Common Multiple. It is used to find the smallest positive integer that is divisible by all the numbers (of which, LCM is calculated). For example, the LCM of 2 and 3 is 6 indicated by:

LCM(2, 3) = 6

As you can see that the number 6 is divisible by both the numbers 2 and 3. LCM (Least Common Multiple) can also be called as:

  • Lowest Common Multiple
  • Least Common Divisor

Meaning of both is same, that is to find the number that will be divisible by the given numbers (to which the LCM to be calculated).

How to Find LCM ?

To find LCM, there are many methods available. But here, we will only discuss about two popular methods:

  • Listing Multiples Method
  • Ladder Method

Listing Multiples Method

To find LCM using listing multiples method, we have to follow the algorithm given below:

  • Write down the multiple of all given numbers
  • Find the smallest number, that is available in every number's multiples
  • This smallest number is the LCM

For example, to find LCM of 10, 12, 15. Then using list multiples method, we have its mutiples as:

  • Multiples of 10: 10, 20, 30, 40, 50, 60, ..
  • Multiples of 12: 12, 24, 36, 48, 60, 72, ..
  • Multiples of 15: 15, 30, 45, 60, 75, 90, ..

Because 60 is available in all multiples list, therefore it is the answer. So we can write:

LCM(10, 12, 15) = 60

Ladder Method

This method to find LCM, is undoubtly a very popular method. It is also the easiest way to find out the LCM of two or more than two numbers. So to find LCM of 10, 12, 15 using ladder method, here is its step by step solution:

find lcm

I hope, you are familiar with above method. If you're not, then here are some main steps:

  • List out all the numbers
  • Divide the number with least to maximum (equals to the number) until all quotient becomes 1
  • That is, start with 2
  • Check if 2 divides any of the given number
  • If it divides, then proceed and write down the quotient of the number (divided by 2) in second line
  • Otherwise check if 3 divides any of the given number
  • If it divides, then proceed. Otherwise check for next one
  • Here, the quotient of number (if gets divided) will be written in next line and rest of the number will be written as it is
  • Process in this way, until every quotient becomes 1

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