# Least common multiple calculator

**Usage:**

Enter the two numbers whose lcm is to be calculated and then click on "Calculate".

# Least common multiple - What does it mean?

The least common multiple (lcm) is a mathematical term. It is the smallest positive natural number that is a multiple of two numbers. It is at least the larger of the two numbers and at most the product of both. The lcm is used mainly in fractions, but also in number theory.

In fractions, it is used to "expand" fractions, for example, to add them together.

"Expanding" means that 2 fractions are brought to the same denominator, keeping this denominator as small as possible, instead of simply multiplying both denominators together. The smallest possible common denominator is also called the main denominator.

# How is the least common multiple calculated?

For the calculation of the lcm there are 2 possibilities, on the one hand the prime factorization of both numbers and on the other hand over the so-called Euclidean algorithm. With the calculation by means of a prime factorization one takes the prime factors of the larger number and the prime factors of the smaller number which did not occur with the larger number and multiplies all with each other.

However, this process is very time-consuming, especially for large numbers, so a more efficient method is used for such numbers, with the help of the so-called Euclidean algorithm. Since the lcm of two numbers is the quotient of their product and their lcm, the Euclidean algorithm can also be used to determine the lcm by multiplying both numbers together and then dividing by their greatest common divider.

Our online calculator uses the Euclidean algorithm method to determine the lcm. Simply enter the two numbers whose lcm you want to determine and click "Calculate".

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