LCM Calculator: Find Least Common Multiple

An LCM Calculator is available online for free to help you quickly find the Least Common Multiple (LCM) of two or more numbers. The LCM is the smallest positive number which can be divided by the given numbers without leaving a remainder.

Finding the LCM of a number is an important part of maths and can be used when working with fractions, multiples, divisors and patterns. Whilst you can work out the LCM manually, using times tables and prime factors, using an online LCM Calculator will make it quicker and easier.

As an example, if we want to find the LCM of 4 and 6, we would look at the multiples:

Multiples of 4: 4, 8, 12, 16, 20, 24…

Multiples of 6: 6, 12, 18, 24, 30…

The smallest common multiple is 12, so the LCM of 4 and 6 is 12.
Our LCM Calculator makes it easy for students, teachers, parents and professionals to find the LCM of multiple numbers in seconds. Simply type in your numbers and press the calculate button to give you an accurate answer.

Useful for school work, fractions and number patterns.

How to Use an LCM Calculator

Using an online LCM Calculator is easy and does not require any advanced mathematical knowledge.

• Enter your numbers – Type in two or more positive whole numbers.
• Double check your numbers – Ensure that all your numbers are correct.
• Press calculate – Press the calculate button.
• Your Answer – The LCM of your numbers will be shown.
• Clear – Clear your previous numbers and calculate new numbers.

For example, if you type in 8 and 12, the LCM will be 24.

Useful for quick calculations and reduces error in manual calculations.

LCM Calculator Formula

There are a variety of ways to find the LCM of numbers including prime factors and GCD.

One of the most commonly used formulas for finding the LCM of two positive integers is:

LCM(a,b)=|a x b| / GCD(a,b)
Where:

a – First number.

b – Second number.

GCD – Greatest Common Divisor.

LCM – Least Common Multiple.

The Greatest Common Divisor is the largest positive integer that can divide the two numbers without leaving a remainder.

To find the LCM of three or more numbers:
LCM(a,b,c)=LCM(LCM(a,b),c)

And this can continue for more numbers.

Prime Factors

Another way to find the LCM is using prime factors.

• Break down into prime factors – Find the prime factors of each number.
• List all different prime numbers – List all the different prime numbers.
• Highest power – Choose the highest power of each prime factor.
• Multiply – Multiply the prime factors together.

This is useful for multiple numbers.

Example

Let us understand how to find the LCM with an example.

Example – Find the LCM of 12 and 18.

Find prime factors:

Prime factors of 12:

12=2^2 x 3

Prime factors of 18:

18=2 x 3 2

Choose the highest power:

Highest power of 2 = 2²

Highest power of 3 = 3²

Multiply:

LCM = 2 2 x 3 2

LCM = 4 x 9

LCM = 36

\\(\\text{LCM}(4,6)=12\\)

Three jumps of 4 and two jumps of 6 meet at 12.

\\(A\\)

\\(B\\)

Feedback

Visual example – The first common positive multiple of 4 and 6 is 12.

Using GCD formula:

GCD of 12 and 18 = 6.

LCM = (12 x 18)/6

LCM = 216/6 = 36

The LCM of 12 and 18 is 36.

What does your answer mean?

The answer provided by the LCM Calculator is the smallest positive integer that can be divided by all numbers you have entered.

For example, if the LCM of 12 and 15 is 60, this means:

60 ÷ 12 = 5

- 60 ÷ 15 = 4

Both calculations will give whole numbers and no remainders.

It is important to understand what your answer means as the LCM is not simply multiplying all the numbers together. It is the smallest common multiple.

For example, 12 multiplied by 15 is 180 however the LCM is only 60.

The smaller the LCM, the earlier you have found the number that meets all the criteria.

Factors that affect your answer

There are many factors that can affect the LCM of two or more numbers.
Size of numbers

Larger numbers can lead to a larger LCM. However this depends on the relationship between the numbers.

Common factors

Numbers with common factors will often have a smaller LCM.

For example, 8 and 12 have a common factor of 4. This means their LCM is 24 rather than 96.

Prime factors

The LCM will depend on the prime factors of each number. The highest power of all prime factors needed will be included.

Number of values

If you are finding the LCM for more than two numbers, you may get a larger answer.

Multiples

If one number is a multiple of the other, the larger number will be the LCM.
For example, the LCM of 5 and 20 is 20.

Zero and negatives

Typically, LCM calculations are done using positive integers. However, some mathematical rules state that an LCM containing zero will be zero.

Depending on the calculator, zero may be handled differently. Negative numbers are commonly converted into their absolute value.

Benefits and Practical Uses

An online LCM Calculator can offer many benefits.

Saves time

Calculating the LCM manually can take time. Using the LCM Calculator will give you an answer almost instantly.

Helps students learn maths

Students can use the LCM Calculator to check answers to homework, understand multiples and practise number theory.

Helps with fractions

The LCM is often used to find the lowest common denominator when adding or subtracting fractions with different denominators.

For example, to add 1/4 and 1/6 you need to find the LCM of 4 and 6 which is 12.

Helps with scheduling

The LCM can help you work out when recurring events will happen.
For example, if one event happens every 4 days and another every 6 days, they will both happen together again after 12 days (assuming they start on the same day).

Can help with problem solving

Teachers, parents and students can use the LCM to solve problems involving divisors, number patterns and common multiples.

Reduces error

The LCM Calculator removes many repetitive calculations and will give you consistent answers.

Easy to use

The online LCM Calculator can be used on a computer, tablet or smartphone.

Accuracy, Assumptions and Limitations

The LCM Calculator will give you accurate answers as long as you enter valid values and it is using an accurate LCM algorithm.

There are some assumptions and limitations.

• Whole numbers – LCM calculations are typically done with integers.
• Positive numbers – Most LCM calculators for education will expect positive whole numbers.
• Zero – Zero may be handled differently.
• Negative numbers – Some LCM Calculators will automatically convert to absolute values whilst others may not allow negative numbers.
• Large numbers – If you enter very large numbers, it may go beyond the range of numbers the calculator can handle.
• Incorrect numbers – Entering incorrect numbers will give you an answer that doesn’t match your calculation.

Whilst the LCM Calculator will give you the mathematical answer, it won’t explain the process unless it has a step by step option.

It is useful to know about prime factors and GCD.

FAQs

What is an LCM Calculator?

An LCM Calculator is an online mathematical tool that can be used to find the Least Common Multiple of two or more numbers. This is the smallest positive number that all the numbers you have entered can divide into without leaving a remainder.

How do you find the LCM of two numbers?

The LCM can be found using prime factors or the GCD formula. The formula is LCM(a, b) = |a x b| ÷ GCD(a, b). Alternatively you can list the multiples of both numbers and find the smallest common multiple.

What is the LCM of 4 and 6?

The LCM of 4 and 6 is 12. Multiples of 4 are 4, 8, 12, 16. Multiples of 6 are 6, 12, 18. The smallest common multiple is 12.

Can I find the LCM of more than two numbers?

Yes. To find the LCM of three or more numbers find the LCM of two numbers, then use that number with the next number. Continue until you have included all numbers.

What is the difference between LCM and GCD?

The LCM stands for Least Common Multiple. This is the smallest positive number that all the given integers can divide into. The GCD stands for Greatest Common Divisor. This is the largest positive integer that can divide all the given integers without leaving a remainder. Both are important in number theory and fractions.