LCM and GCF 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) and greatest common factor (GCF).

How to find the LCM and GCF?

There are two sets of factors and multiples worksheets.

• LCM & GCF (Two Numbers).
• LCM & GCF (Three Numbers).

To find both the least common multiple (LCM) and greatest common factor (GCF) of two or more numbers, you can follow these steps:

1. List the Prime Factors
   Find the prime factorizations of each number.
2. Identify All Prime Factors and Highest Exponents
   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. Find the Highest Exponent for Each Prime Factor
   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. Calculate the LCM and GCF
   To calculate the LCM, multiply together all the prime factors found in Step 3, each raised to its corresponding highest exponent.
   To calculate the GCF, multiply together all the common prime factors raised to their corresponding lowest exponents.

Example: Find the LCM and GCF of 18, and 24.

Step 1: List the Prime Factors
Prime factorization of 18: 2¹ × 3²
Prime factorization of 24: 2³ × 3¹ 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 3 (from 2³ in the prime factorization of 24).
For the prime factor 3: The highest exponent is 2 (from 3² in the prime factorization of 18).
4. Calculate the LCM and GCF
LCM = 2³ × 3² = 72
GCF = 2¹ × 3¹ = 6
So, the LCM of 18, and 24 is 72, and the GCF is 6.

Using this method, you can efficiently find both the LCM and GCF of multiple numbers by considering their prime factorizations.

Have a look at this video if you need to review how to find the GCF and LCM.

• How to Find the GCF and LCM using Prime Factorization

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more LCM & GCF Worksheets.

 

More LCM and GCF Worksheets

Printable
(Answers on the second page.)
LCM and GCF Worksheet #1 (Two Numbers)
LCM and GCF 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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