6th Grade Math · Greatest Common Factor and Least Common Multiple
Mixed practice Worksheets
Fresh practice, ready to print. Answer key included.
GCF and LCM on the same page. The label says which one.
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Or start with a ready-made version.
How it works: a quick refresher
The rules this worksheet practices, then one problem worked from start to finish.
| Strategy | How it works |
|---|---|
| List the factors | GCF of 18 and 24: factors of 18 are 1, 2, 3, 6, 9, 18. Factors of 24 include 1, 2, 3, 4, 6, 8, 12, 24. The greatest number on both lists is 6. |
| Or use prime factors | 18 = 2 × 3 × 3 and 24 = 2 × 2 × 2 × 3. The shared primes are 2 × 3 = 6, and that is the GCF. |
| LCM from the lists | Multiples of 4: 4, 8, 12, 16. Multiples of 6: 6, 12, 18. The least number on both lists is 12. |
| LCM from primes | 4 = 2 × 2 and 6 = 2 × 3. Take every prime the most times it appears: 2 × 2 × 3 = 12. |
| GCF times LCM | For the same two numbers, GCF × LCM equals their product. For 4 and 6, the GCF is 2 and the LCM is 12, and 2 × 12 = 4 × 6. |
Worked example
Find the GCF of 18 and 24.
- 118 = 2 × 3 × 3.
- 224 = 2 × 2 × 2 × 3.
- 3The primes in both are 2 and 3.
- 42 × 3 = 6, so the GCF is 6.
Ready-made versions
Three fixed versions you can link to or share. Each is a PDF with its own answer key.
- Mixed practice Worksheets, version 1Worksheet PDFAnswer key PDF
- Mixed practice Worksheets, version 2Worksheet PDFAnswer key PDF
- Mixed practice Worksheets, version 3Worksheet PDFAnswer key PDF
Grade level and standard
Written for 6th grade math (number system) and aligned to CCSS 6.NS.B.4. It also works as review in later grades.
Common questions
- Is there an answer key?
- Yes. Every worksheet has a matching answer key with each answer worked on the same grid or layout as the question. The worksheet ID printed at the bottom of each page pairs a sheet with its key.
- What does GCF(18, 24) mean?
- It is short for the greatest common factor of 18 and 24. LCM(4, 6) means the least common multiple of 4 and 6. Textbooks use both ways of writing it.
- Why is the GCF never 1 on these pages?
- A GCF of 1 means the numbers share no prime factor, which is a quick special case. These problems always share a factor of 2 or more so there is something to find.
- How many different versions are there?
- About a million per skill. Each time you press the button the problems are generated fresh, so you can print a different version for every student, a retake, or another night of practice.
- Are the worksheets free?
- Yes. They are free to print and copy for your home or classroom, with no sign-up.