6th grade GCF and LCM
6th grade GCF and LCM (class 6): a quiz for kids, then every skill in order with lessons, a checklist and a plan.
🧒 Kids: answer 10 grade 6 questions on factors and multiples. Read each one, then tap Check ✓!
🔢 Factors practice 🏆 Factors levels 🧮 GCF and LCM calculator
What children learn about factors in 6th grade
In grade 6, children find the greatest common factor of two numbers up to 100 and the least common multiple of two numbers up to 12, and use the GCF to rewrite sums with the distributive property.
- 6.NS.B.4: find the greatest common factor of two whole numbers up to 100.
- 6.NS.B.4: find the least common multiple of two whole numbers up to 12.
- 6.NS.B.4: use the distributive property to write a sum with a common factor, like 36 + 8 = 4(9 + 2).
- 6.EE.A.1: write and evaluate whole-number exponents, used in prime factorization.
Other grades: 4th grade · 6th grade
The big idea in grade 6
Grade 6 puts factors and multiples to work (6.NS.B.4). Children find the greatest common factor of two numbers up to 100. They find the least common multiple of two numbers up to 12.
They also use the GCF with the distributive property, rewriting 36 + 8 as 4(9 + 2). This is the first step towards factoring in algebra.
Prime factorization, written with exponents like 72 = 2³ × 3², links this unit to the exponents unit. It gives a fast way to find the GCF and LCM of big numbers.
The hardest part is not the arithmetic. It is deciding whether a word problem needs the GCF or the LCM.
When your child gets stuck
Most grade 6 trouble is mixing up the GCF and LCM. Use the size check: the GCF is never bigger than the smaller number, and the LCM is never smaller than the bigger number.
If the LCM always comes out as the two numbers multiplied, show 6 and 8. 48 is a common multiple, but 24 is the least one.
If factor trees go wrong, check that every circled number is prime. 72 = 2 × 4 × 9 is not finished.
6th grade GCF and LCM skills, in order
Work down the list. Each lesson explains the idea for parents with pictures and has a quiz for your child.
By the end of grade 6, your child should be able to…
- Write 72 as a product of primes: 2³ × 3².
- Find the GCF of 24 and 36 (12) in two different ways.
- Find the LCM of 6 and 8 (24), and explain why it isn’t 48.
- Rewrite 36 + 8 as 4(9 + 2).
- Decide whether a story needs the GCF or the LCM.
- Simplify 18/24 in one step with the GCF.
Unsure where your child is? The factors and multiples levels page has a short test for every step from factor pairs to word problems.
A 4-week plan for 6th grade GCF and LCM
| When | Focus |
|---|---|
| Week 1 | Factor trees and prime factorization with exponents |
| Week 2 | Common factors and the GCF, then simplifying fractions |
| Week 3 | Common multiples and the LCM, then common denominators |
| Week 4 | GCF and LCM word problems and the distributive property |
Add 5 minutes a day with the factors and multiples practice tool, and check answers with the GCF and LCM calculator.
More for grade 6
All 6th grade math · CBSE class 6: Prime Time · 6th grade ratios · Factors and multiples quiz for grades 4 to 6 · Factors and multiples for kids
What to say to your child
A short script for teaching it the first time. Pause after each line and let your child do the next step.
- “What is the biggest number that divides 24 and 36?” (12.)
- “How did you find it?” (Listed the factors, or used primes.)
- “Buses every 6 and 8 minutes. When do they meet again?” (24 minutes.)
- “Is that the GCF or the LCM?” (LCM: things happening together.)
- “Write 36 + 8 with the GCF outside brackets.” (4(9 + 2).)
More worked examples
Example 1: GCF
GCF(30, 45): 30 = 2 × 3 × 5 and 45 = 3² × 5 share 3 × 5, so the GCF is 15.
Example 2: LCM
LCM(9, 12): multiples of 12 are 12, 24, 36. 36 is a multiple of 9, so 36.
Example 3: distributive property
42 + 56 = 14 × 3 + 14 × 4 = 14(3 + 4), because the GCF is 14.
Practice questions (answers below)
Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.
- GCF of 16 and 24
- GCF of 27 and 45
- LCM of 4 and 10
- LCM of 8 and 12
- Prime factorization of 60
- Rewrite 18 + 30 with the GCF
- Simplify 24/36
- Least common denominator of 1/6 and 1/9
- 20 pens and 30 pencils in identical packs, none left: most packs?
- Stretch: GCF and LCM of 12 and 18, then multiply them
Show the answers
- 8
- 9
- 20
- 24
- 2² × 3 × 5
- 6(3 + 5)
- 2/3
- 18
- 10 (GCF)
- 6 × 36 = 216 = 12 × 18
Common mistakes
How to teach it at home
Five minutes a day
Short daily practice beats long weekend sessions.
Use real things
Counters, eggs in boxes, chocolate bars and packs of pens all show factors and multiples.
Ask how
Ask “how do you know?” after each answer. Explaining builds understanding faster than speed drills.
By grade
- Before: 4th grade factors and multiples
- After: adding fractions and exponents
Not sure where to start?
The free 6th grade math check-up tests every grade 6 topic in 18–22 minutes. It shows which topics are solid and which lesson to start with.
Worksheets and practice
Greatest common factor worksheet: printable PDF with an answer key.
Last reviewed
Questions parents ask
What do 6th graders learn about GCF and LCM?
The greatest common factor of two numbers up to 100, the least common multiple of two numbers up to 12, and using the GCF with the distributive property (6.NS.B.4).
What is the easiest way to find the GCF and LCM?
For small numbers, list factors or multiples. For bigger numbers, use prime factorization or the ladder method, which gives both at once.
Is there a 6th grade GCF and LCM quiz?
Yes. The quiz at the top of this page has 10 mixed grade 6 questions, each marked straight away. Play again for a fresh set, or try the factors and multiples quiz for grades 4 to 6.
What is taught about factors in class 6 in India?
NCERT class 6 covers factors, multiples, primes and prime factorization in chapter 5, Prime Time. This page lists the skills in order, starting with prime factorization, common factors.
How much practice does a 6th grader need?
About 10 minutes a day: one short round with the practice tool and one question worked on paper. Short daily practice works better than long weekly sessions.