This guide and this page are intended for our readers to learn how to find the lowest common multiple -LCM of two or more numbers.
LCM
Determining the lowest common multiple is one of the most used procedures that is used as an additional procedure when practicing mathematical calculations or mathematical operations. It is most often used when adding fractions that have different denominators, so the first step in solving this type of problem is determining the lowest common denominator, which is just another synonym for the lowest common multiple. For this mathematical data for two, three, four, or more numbers, the abbreviation LCM – lowest common multiple is used.
In the text below you can see several different examples of determining the lowest common multiple of different numbers.
Let’s start with the simplest situation we need to solve:
How To Find The Lowest Common Multiple Of Two Numbers
Consider the first example that shows the procedure we need to follow to determine the LCM of two numbers.
Example 1: Determine the LCM of the numbers 2 and 8!
When determining the LCM of the numbers 2 and 8, we need to decompose the numbers into multiples. In this breakdown, it is clear that:
2=2×1
8=2x2x2
To get the lowest common factor of the numbers 2 and 8, we multiply all the prime factors from which these numbers are composed, and we write those that are repeated in both numbers only once. Therefore it is valid that:
LCM (2;8) = 2x2x2=8
And indeed, the number 8 is the smallest possible number that can be divided by both the number 2 and the number 8.
How To Find The Lowest Common Multiple Of Three Numbers
The same procedure applies if we want to determine the LCM of three or more than three numbers. The only difference concerns the work with more numbers, their decomposition and the longer procedure that we have to realize in practice! Look at the example with number 2!
Example 2: Determine the LCM of the numbers 4, 6 and 18!
Of course, we approach this situation in the same way. Let’s factor all three numbers into their prime factors. By appropriate decomposition it is obtained that:
4=2×2
6=2×3
18=2x3x3
To determine the LCM of the numbers 4, 6, and 18, we multiply all their prime factors together, but we are careful to write those that are contained in more than one number only once. Thinking in this way we get that:
LCM (4;6;18) = 2x2x3x3=36
It is nice to make a check when obtaining the lowest common multiple, which will confirm that the obtained numerical value is divisible by all single numbers:
36:4=9
36:6=6
36:18=2
We note that indeed the number 36 is the lowest common multiple of the numbers 4, 6 and 18.
The technique used in the correctly solved examples above on the page can be generalized, so we use the same procedure if we want to determine the LCM of more than three numbers, no matter what their exact number is!
Second Method – Video Examples
In the video presented below, you can see an additional method of determining LCM with a shortened procedure! The rule of this second method is easy to see. Therefore, we recommend that you watch the video in detail and all the examples presented in it to draw a conclusion about which procedure is easier and more practical for you. In the end, as in many other math problems, you can arrive at the same solution no matter which procedure you use. Of course, whatever procedure you decide on, be sure to use it in the right way!
We look forward to your additional questions related to additional ambiguities that you would like us to explain to you!
