LCM Calculator — Least Common Multiple

The LCM calculator will determine the least common multiple of two to fifteen numbers for you — no need to fret! This calculation is essential when adding or subtracting fractions with different denominators (check the adding fractions calculator if you want to do it with a dedicated tool). The following text will explain what is LCM, how to find the least common multiple, and how to use the least common multiple calculator.

Are you working with fractions? Be sure to visit the LCD calculator, which finds the least common denominator in no time!

The LCM is the least common multiple or lowest common multiple of two or more numbers. We can find the least common multiple by breaking down each number into its prime factors. This can be accomplished by hand or by using the factor calculator or prime factorization calculator. The method for finding the LCM, along with an example illustrating the method, will be seen in the next section.

Take each number and find its prime factors. Knowing various divisibility rules helps assist in this process.

1. Any even number is divisible by 2.
2. Any number whose sum of the digits is divisible by 3 is also divisible by 3.
3. A number is divisible by 4 if the last two digits of the number form a number divisible by 4.
4. All numbers ending in 5 or 0 are divisible by 5.
5. A number is divisible by 6 if it is divisible by both 2 and 3.
6. A number is divisible by 8 if the last three digits of the number form a number divisible by 8.
7. A number whose digits sum to a number divisible by 9 is also divisible by 9.
8. Any number ending in 0 is divisible by 10.

Once the numbers are broken down into their prime factors, multiply the highest power of each factor to get the LCM.

We are going to show how to find the LCM of 24, 80 and 121. First, we'll get the factors of each number. These are:

24 = 2 × 2 × 2 × 3
80 = 2 × 2 × 2 × 2 × 5
121 = 11 × 11

Gather all the factors, so we have 2, 3, 5, 11. Next, multiply the highest power of each of these factors. That gives us:

2 × 2 × 2 × 2 × 3 × 5 × 11 × 11 = 29,040

The LCM calculator can be used to check your answer or simply perform this calculation for you.

Just as you need prime factorization to get the LCM, it's equally important to find the GCF, which is the greatest common factor. To find the GCF, take the product of all the common factors of each number. For example, the GCF of 16 and 50 is 2 since the only factor in common between the two numbers is 2. The GCF calculator is a handy tool to calculate this.

Note that the LCM of two integers is the smallest positive integer divisible by both the integers. This is only true if both the integers are not zero. The LCM calculator will display a value of zero whenever at least one number is zero.

In 2024, the US witnessed a very unusual phenomenon eagerly picked up by media outlets. Its main protagonists were cicadas. While not particularly dangerous to humans, cicadas can be very, very loud, suddenly teeming with life in otherwise quiet areas. When cicadas are not there, you may be unaware of their existence, but when they come around, it is impossible to miss the never-ending noise they produce.

Cicadas spend many years underground — 13 or 17, depending on the brood — before they crawl out on the surface. Both 13 and 17 are prime numbers, and so their least common multiple is 221, their product. That means it is extremely rare for two broods to come out at once; this happens precisely every 221 years. 2024 was one of these extraordinary years when both broods of cicadas swarmed across the American Southeast and Midwest.

Their presence was particularly felt in Illinois, a US state that marks the boundary between two broods. The previous time both broods emerged simultaneously was in 1803, when Thomas Jefferson, one of the Founding Fathers of the United States, was the president.

The LCM of 18 and 24 is 72.

The simplest way to determine the LCM of two numbers is by listing their multiples until you reach a common multiple.

Multiples of 18: 18, 36, 54, 72, 90, 108, 126...

Multiples of 24: 24, 48, 72, 96, 120, 144...

So, the first one common among them is 72.

There are different methods to determine the LCM.

1. List of multiples: List the multiples of the numbers. Pick the least multiple common among all the numbers.

2. Prime factorization: Express all numbers as a product of their prime factors. For each prime, pick its highest power and multiply them all together.

3. Using the GCF: The formula for the GCF method is:

   LCM(a,b) = |a·b| / GCF(a,b)

4. Table/Ladder method: Write the numbers in a row and divide by prime numbers. Keep going until you reach a prime number for each. Find the product of all the prime numbers.

A fraction comprises two elements, the numerator and the denominator. The formula to determine the LCM of fractions is:

LCM = LCM of numerator / GCF of denominator

For instance, the two fractions are 2/3 and 4/5. The numerators are 2 and 4. The denominators are 3 and 5.

LCM = LCM(2,4)/ GCF(3,5)

LCM = 4 / 1

LCM = 4

The LCM of 2, 4, 6, 8, 10, and 12 is 120. Let's see how we can get the LCM by prime factorization.

1. First, determine the prime factors of all the numbers:

   2: 2¹

   4: 2 × 2 = 2²

   6: 2 × 3 = 2¹ × 3¹

   8: 2 × 2 × 2 = 2³

   10: 2 × 5 = 2¹ × 5¹

   12: 2 × 2 × 3 = 2² × 3¹

2. Find the highest power of each prime number and multiply them together:

   2³ × 3¹ × 5¹ = 120