Least Common Multiple Game
The least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of all the numbers involved.
This is essential for tasks like finding the lowest common denominator (LCD) to add fractions or [subtract fractions](/subtract-fractions-game.html.
 
To find the Least Common Multiple (LCM) of two numbers, you can list the multiples for each number and identify the smallest number that appears in both lists. Alternatively, you can use prime factorization, where you break down each number into its prime factors and then take the highest power of each prime factor that appears in either factorization and multiply them together to get the LCM. A third method would be to use repeated division. Scroll down the page for a more detailed explanation.
 
This Least Common Multiple Game allows you to select the number of terms to customize the difficulty of the game. If you give a wrong answer, the game will provide the correct answer.
 

Least Common Multiple

Find the LCM.

Number of Terms:

2 Numbers

3 Numbers

Enable 60-Second Timer

Start Game

Score: 0 / 0

Time: 60

What is the LCM of:

Check Next

Back to Menu

 

How to Play the Least Common Multiple Game
The game is designed to help you practice your skills in a fun environment.
Here’s how to play:

1. Number of Terms: Select either two or three terms.
   
2. Timed Option: Check the timer if you want to enable the 60 second timer. Click “Start Game”.
   
3. Look at the Problem: You’ll see two or three numbers at the top of the box. Your goal is to find the least common multiple of the numbers.
   
4. Enter Your Answer: Type your answer into the box.
   
5. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
6. Get a New Problem: Click the Next button (or press Enter again) for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
7. Back to Menu Click “Back to Menu” to restart the game.
    
   

How to Find the Least Common Multiple
Least Common Multiple Lesson
There are a couple of ways to find the LCM. The most straightforward method is to list the multiples of each number and find the least one they have in common.
Listing Multiples

1. List the multiples: of each number by skip-counting or multiplying the number by 1, 2, 3, and so on.
   
2. Identify common multiples: by looking for numbers that appear in both lists.
   
3. Choose the smallest: common multiple from the shared numbers; this is the LCM.
   Example: Find the LCM of 6 and 10.
   Multiples of 6: 6, 12, 18, 24, 30, 36…
   Multiples of 10: 10, 20, 30, 40, 50…
   The smallest number in both lists is 30, so the LCM of 6 and 10 is 30.
    
   

Using Prime Factorization

1. Find the prime factors: of each number by using a factor tree or other methods.
   
2. List the prime factors: for each number.
   
3. Construct the LCM: by taking the highest power of each prime factor that appears in either factorization.
   
4. Multiply these highest powers: together to get the LCM.
   Example: Find the LCM of 60 and 90.
   Prime factors of 60: 2 × 2 × 3 × 5 (or 2² × 3¹ × 5¹).
   Prime factors of 90: 2 × 3 × 3 × 5 (or 2¹ × 3² × 5¹).
   The highest power for each factor is 2², 3², and 5¹.
   LCM = 2² × 3² × 5¹ = 4 × 9 × 5 = 180.
    
   

Using Repeated Division
To find the Least Common Multiple (LCM) using repeated division, write the numbers in a row, then repeatedly divide them by the smallest prime number that divides at least one of the numbers, bringing down any numbers that aren’t divisible. Continue this process until all the numbers at the bottom are 1. The LCM is the product of all the divisors on the left and any remaining numbers at the bottom.

The video gives a clear, step-by-step approach to walk through the process of finding the Least Common Multiple.

• Show Video

 

Free Fraction Games
Learning Fractions	Equivalent Fractions	Compare Fractions
Simplify Fractions	Greatest Common Factor	Least Common Multiple
Improper Fractions & Mixed Numbers	Add Fractions	Subtract Fractions
Subtract Fractions from Whole Numbers	Multiply Fractions	Divide Fractions
Multiply Fractions & Whole Numbers	Divide Fractions & Whole Numbers	Add Mixed Numbers
Subtract Mixed Numbers	Multiply Mixed Numbers	Divide Mixed Numbers

 

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