Least Common Multiple


The Least Common Multiple (LCM) is the smallest number, other than 0, that is a multiple of 2 or more numbers. To better understand this definition, we will look at all the terms:

Multiple: Multiples of a number are what you get when you multiply it by other numbers.

Let’s look at an example of the multiples of 2 and 3. To calculate your multiples, you need to multiply the 2 or 3 by 1, by 2, by 3, etc.

2 x 1 = 2 2 x 2 = 4 2 x 3 = 6 2 x 4 = 8 and so on up to infinite numbers.

3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 and so on up to infinite numbers.

Common Multiple: A common multiple is a number that is a multiple of two or more numbers at the same time, that is, it is a common multiple of those numbers.

Continuing with the previous example, let’s look at the common multiples of 2 and 3.

Least Common Multiple: The Least Common Multiple is the smallest number of common multiples.

Continuing with the previous example, if the common multiples of 2 and 3 were 6, 12, and 18, the Least Common Multiple or LCM is 6, since it is the smallest of the common multiples.

Next we will see how to calculate the least common multiple. You can use two methods.

The first method to calculate the lcm is the one we used before, that is, we write the first multiples of each number, we indicate the multiples that are common and we choose the smallest common multiple.

Now let’s explain the second method for calculating the LCM. In this case, the first thing to do is divide each number into prime factors. Then, we will have to choose the common and uncommon factors raised to the maximum exponent and, finally, we will have to multiply the chosen factors.

Another use of the LCM is in the field of algebraic expressions. The LCM of two of these expressions is equivalent to the one with the smallest numerical coefficient and the lowest degree that can be divided by all the given expressions without leaving a remainder.