Least Common Multiple Calculator Online

The LCM Calculator will help you to find the smallest positive number in which all of the numbers you enter into it can divide into without leaving a remainder. This can be helpful when doing maths homework, fractions, creating recurring schedules and much more.

What is the Least Common Multiple?

Also known as the Lowest Common Multiple, the LCM is the lowest common multiple which can be divided by multiple numbers.

For example, the multiples of 4 are 4, 8, 12, 16, 20, 24 etc. The multiples of 6 are 6, 12, 18, 24, 30 etc. The smallest positive number that appears in both of these lists is 12, therefore the LCM of 4 and 6 would be 12.

By using our LCM Calculator you can enter 2 or more positive whole numbers and instantly get the LCM. This calculator will do all of the calculations for you.

This calculator can be used by students, teachers, parents, engineers and anyone else needing to do maths problems.

How to Use the LCM Calculator

Our LCM Calculator is simple to use. Just follow the steps below to calculate the LCM of two or more numbers.

Enter the first number

Enter the next number(s).

Double check your numbers are correct.

Click calculate.

The LCM will be shown.

For example if you enter 8 and 12 the LCM will be calculated.
This can help you with fractions, recurring patterns and various maths problems.

LCM Formula

There are multiple ways to calculate the LCM of numbers. The most commonly used methods are using the Greatest Common Divisor and Prime

Factors.

LCM Using the GCD Formula

To calculate the LCM of two positive integers use the formula below.

LCM(a,b) = |a × b| / GCD(a,b)

Where:

LCM = Least Common Multiple

a = First number

b = Second number

GCD = Greatest Common Divisor of both numbers. This is the largest positive integer which can divide both numbers.

LCM Using Prime Factors

To calculate the LCM using Prime Factors, you need to calculate the prime factors of each number. Then choose the highest power of each prime number.

For example:

12 = 2^2 x 3

18 = 2 x 32

Choose the highest powers.

LCM = 22 x 32

LCM = 4 x 9 = 36

Therefore the LCM of 12 and 18 is 36.

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Example Calculation

Let’s see how we can calculate the LCM with an example.

Example 1: LCM of 8 and 12

We are given:

First Number = 8

Second Number = 12

Step 1: Find multiples for each number.

Multiples of 8:

8, 16, 24, 32, 40, 48, 56...

Multiples of 12:

12, 24, 36, 48, 60...

Step 2: Find common multiples.

Common multiples are 24, 48, 72 etc.

Step 3: Find the lowest positive common multiple.

The lowest common multiple is 24.

Answer:

LCM (8, 12) = 24

Example 2: LCM of 15 and 20 using the GCD Formula

We are given:

First Number = 15

Second Number = 20

GCD = 5

Use the formula:

LCM(a,b) = (a × b) / GCD(a,b)

Plug in our numbers:

LCM(15, 20) = (15 × 20) / 5

= 300 / 5

= 60

Answer:

LCM (15, 20) = 60

Meaning 60 is the lowest positive number that both 15 and 20 can divide into.

Understanding your result

Once you have entered your numbers into the LCM Calculator, it will show you the lowest positive number that all of your numbers can divide into.
Understanding your answer will help you use it in other maths problems.

Some key points to note:

LCM: The lowest positive common multiple of all your numbers.

Common Multiples: Numbers that can be divided evenly by your numbers.
Prime Factors: Prime numbers used in the calculation.

GCD: Greatest Common Divisor. This helps you calculate the LCM using a formula.

Divisible: The final LCM must be divisible by all of the numbers you have entered.

For example if the LCM of 12 and 18 says 36, then dividing 36 by each number will give you a whole number.

36 / 12 = 3

36 / 18 = 2

Meaning its a common multiple.

Factors affecting your result

There are a couple of factors that affect the LCM.

Numbers Entered

The numbers you enter will affect the LCM. If you change either number, it could change the result.

Prime Factors

The prime factors of your numbers will affect the LCM. You will need to include the highest powers of all the prime factors needed.

GCD

The GCD will affect the LCM. When using the product and GCD formula, the higher the GCD the lower the LCM.

Number of Numbers Entered

If you are calculating the LCM of 3 or more numbers then the LCM must be divisible by all of them.

Relationship Between Numbers

If one number is a multiple of another, then the LCM will be the largest number. For example, the LCM of 5 and 20 would be 20.

Zero/Negative Values

Typically LCM will be calculated using positive integers. However if you enter a zero or negative, you may need to treat it differently or it may not be within the range of the calculator.

Advantages and Uses of an LCM Calculator

There are many advantages to using an LCM Calculator.

Save Time

You can quickly find the LCM of 2 or more numbers.

Helps with Learning Maths

Students can use this to understand Prime Factors, Divisibility, Common Multiples and Relationships between numbers.

Simplify Fractions

The LCM can help you find the lowest common denominator.

Help with Scheduling

You can use the LCM to work out when recurring events will occur. For example, if two events occur every 6 and 8 days, they will occur together again after 24 days.

Help with Maths Problems

Teachers and students can use the LCM for maths problems such as arithmetic, number theory and more.

Help with Recurring Patterns

The LCM can help you work out when recurring patterns will occur.

Reduce errors

The calculations will be done for you so there is less chance of error.

Accuracy, Assumptions & Limitations

As long as you enter valid numbers, the LCM Calculator will give you an accurate result. However there are a few things to consider.

• Positive Integers: Typically LCM will be calculated using positive integers.
• Incorrect Number: If you enter incorrect numbers then you will get an incorrect result.
• Zero: Sometimes the LCM of zero and a positive integer will be zero.
• However many calculators will not allow you to enter zero.
• Negative Numbers: Typically the LCM will be non-negative. The LCM will usually be calculated using the absolute value of the integers.
• Large Numbers: If you enter very large numbers, they may be out of the range of the calculator.
• More Than 2 Numbers: If you enter more than two numbers then the result must be a common multiple of all numbers.
• Decimal Numbers: The LCM formula for integers does not apply directly to decimal numbers.

For the most accurate result, enter positive integers and double check that the result is divisible by all numbers.

FAQs

1. What is the LCM?

The LCM stands for Least Common Multiple. It is the smallest positive number that can be divided by 2 or more given numbers. For example the LCM of 4 and 6 would be 12.

2. How do I calculate the LCM of 2 numbers?

To calculate the LCM you can list the multiples of each number, use prime factors or the GCD formula. The GCD method uses the formula (product divided by greatest common divisor).

3. What’s the difference between LCM and GCD?

The LCM is the smallest positive number that all of the given numbers can divide into. The GCD is the largest positive number that can divide all of the given numbers. They are commonly used in maths and fractions.

4. Can I calculate the LCM of more than 2 numbers?

Yes! You can calculate the LCM of 3 or more positive integers. The result must be the smallest positive number that can divide into all of the numbers.

5. What is the LCM of 2 numbers where one is a multiple of another?

If one number is an exact multiple of another then the LCM will be the largest number. For example the LCM of 6 and 18 would be 18 as it is already divisible by both numbers.