Least Common Multiple Worksheets

There are six sets of factors & multiples worksheets:

• Factors
  
• Prime Factorization
  
• Greatest Common Factor
  
• Multiples
  
• Least Common Multiple
  
• LCM and GCF
  

Examples, solutions, videos, and worksheets to help Grade 4 students learn how to find the least common multiple (LCM).

How to find the least common multiple?

There are two sets of least common multiple worksheets.

• Least Common Multiple (Two Numbers).
• Least Common Multiple (Three Numbers).

Common Multiple Method
You can find the least common multiple (LCM) of two or more numbers by listing out the multiples of each number and identifying the least common multiple. Here’s a step-by-step guide on how to do this:

1. List the Multiples of Each Number
   For each of the numbers for which you want to find the LCM, start by listing out their multiples. Multiples are obtained by multiplying the number by consecutive positive integers. You can stop listing multiples when you find a common multiple.
2. Identify the Common Multiple
   Look for the smallest (least) common multiple that appears in the lists of multiples for all the numbers you are considering. This common multiple is the LCM.

Example: Find the LCM of 12 and 18 by listing out multiples.

1. List the Multiples of Each Number
   For 12:
   Multiples of 12: 12, 24, 36, 48, 60, 72, …
   For 18:
   Multiples of 18: 18, 36, 54, 72, 90, …
2. Identify the Common Multiple
   From the lists of multiples, we can see that 36 is the smallest (least) common multiple that appears in both lists.
   So, the LCM of 12 and 18 is 36.

Listing out multiples can be a straightforward method for finding the LCM, especially for smaller numbers. However, for larger numbers, the prime factorization method is often more efficient.

Prime Factorization Method

To find the least common multiple (LCM) of two or more numbers, you can use several methods. One common and efficient approach is to use the prime factorization method. Here’s a step-by-step guide on how to find the LCM of two or more numbers using prime factorization:

1. Find the prime factorization of each number by expressing each number as a product of its prime factors.
2. Once you have the prime factorizations, identify all the unique prime factors from all the numbers. This includes all the prime factors that appear in any of the numbers’ factorizations.
3. For each prime factor identified in Step 2, find the highest exponent that appears among all the numbers. This involves selecting the largest exponent for each prime factor.
4. Multiply together all the prime factors found in Step 3, each raised to its corresponding highest exponent. This product is the LCM of the numbers.

Example: Find the LCM of 12 and 18.

1. List the Prime Factors
   Prime factorization of 12: 12 = 2² × 3¹
   Prime factorization of 18: 18 = 2¹ × 3²
2. Identify All Prime Factors
   Unique prime factors: 2 and 3.
3. Find the Highest Exponent for Each Prime Factor
   For the prime factor 2: The highest exponent is 2 (from 2² in the prime factorization of 12).
   For the prime factor 3: The highest exponent is 2 (from 3² in the prime factorization of 18).
4. Multiply the Prime Factors
   LCM = 2² × 3² = 36
   So, the LCM of 12 and 18 is 36.

This method can be extended to find the LCM of more than two numbers by including the prime factorizations of all the numbers and following the same steps. The LCM represents the smallest multiple that is divisible by all the given numbers.

Have a look at this video if you need to review how to find the Least Common Multiple.

• How to Find the LCM using Prime Factorization

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Least Common Multiple Worksheets.

 

More Least Common Multiple Worksheets

Printable
(Answers on the second page.)
Least Common Multiple Worksheet #1 (Two Numbers)
Least Common Multiple Worksheet #2 (Three Numbers)

Online
Prime & Composite Numbers up to 10
Prime & Composite Numbers up to 20

Find Missing Factor
Greatest Common Factor
GCF or HCF

GCF and LCM Word Problems

Related Lessons & Worksheets

Factors & Multiples

More Printable Worksheets

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