LCM Calculator - CalcuNation

Find the least common multiple (LCM) of two numbers with this LCM Calculator.

First Number:
Second Number:

Calculate the least common multiple between two numbers.

What is the Least Common Multiple?

The least common multiple (LCM) between two numbers is the smallest integer that is divisible by both numbers. Sometimes the least common multiple is referred to as the lowest common multiple or the least common denominator.

For example, find the LCM of the two numbers 12 and 16:

The multiples for 12 are 12, 24, 36, 48, 60, 72, 84, 96, etc.

The multiples for 16 are 16, 32, 48, 64, 80, etc.

The two numbers (12 and 16) share many common multiples if you keep expanding on the lists of multiples. But from comparing the two lists, we can see that 48 is the lowest, or least common muliple.

Least Common Multiple Equation

LCM = (a*b) / GCF(a and b)
Use this GCF Calculator to help with this formula

Find the LCM, Least Common Multiple using the Greatest Common Factor

To understand how to use this method, it may be important to familiarize yourself with how to find the greatest common factor.

The greatest common factor between two numbers is the largest factor that both numbers are divisible by. Sometimes the greatest common factor is also referred to as the greatest common divisor (gcd), or the highest common factor (hcf).

For example, find the GCF of the two numbers 12 and 16:
The factors for 12 are 1, 2, 3, 4, 6 and 12. These are factors of 12 because 12 is divisible by all of these numbers. The factors for 16 are 1, 2, 4, 8, 16. The two numbers (12 and 16) share common factors (1, 2, 4). The greatest of these is 4 and that is the greatest common factor.

If using the equation LCM = (a*b) / GCF(a and b).

Let's use the numbers 8 and 12, with 8 being variable (a) and 12 as variable (b). By using the CalcuNation GCF Calculator, we know that the GCF of 8 and 12 is 4. So, our equation comes out to LCM = (8*12) / 4. This calculates out as LCM = 24.

Other LCM Methods

There are other methods to find the least common multiple. While this calculator uses the greatest common factor, you can also use the listing multiples method.

The Listing Multiples method can get lengthy. You literally list out all of the multiples of each number until you find a matching number. The smallest number that matches on the list of multiples is the least common multiple.

There is also the method of Prime Factorization. With this method, you list out all of the prime factors for each number. Then, list all of the prime factors, as many times as they occur for any given number. Then multiply the list of factors together to find the LCM.

The LCM can also be found using the Venn Diagram method, a Cake/Ladder method or Division method.