How to Calculate Least Common Multiple
In this post, we are going to see what the least common multiple is and how to calculate it.
The least common multiple (LCM) of two or more numbers is the smallest number (not counting 0) which is a multiple of all of the numbers.
In order to better understand this definition, we are going to look at all of the terms:
- Multiple: the multiples of a number are the numbers you get when you add a number to itself repeatedly.
- Common Multiple: A common multiple is a number than is a multiple of two or more numbers; in other words, it is a common multiple of all those numbers.
Following with the previous example, we are going to see the common multiples of 2 and 3.
You will see that there are common multiples between two and three, which are emphasized in green in the picture: 6 and12. Keep in mind that the multiples are infinite and we have only shown the first two in this example.
- Least Common Multiple: the least common multiple is the smallest of the common multiples.
Following with the previous example, if the common multiples of 2 and three 3 were 6 and 12, the least common multiple is 6, since it is smaller than 12.
To continue, we are going to see how to calculate the least common multiple. You can use two methods.
First method to calculate the least common multiple:
Is what we used before, in other words, we write the first multiples of each number, we note the multiples that are common and we choose the least common multiple.
Second method to calculate the least common multiple:
The first thing we have to do is break down the prime factors of each number. After, we will have to choose the common factors and not the greatest common to the greatest exponent, and finally, we have to multiple the chosen factors.
We are going to look at an example of this, calculating the LCM of 12 and 8.
We are going to break down 12 and 8 into prime factors:
12 = 22 x 3 8 = 23
Now, we take the highest power of each prime factor in the prime factorization
and multiply them: 23 x 3 = 8 x 3 = 24
So the least common multiple of 12 and 8 is 24.
You can practice some online exercises about LCM and more elementary math in Smartick. Try it for free!