Learning goals
- Factors divide a number with no remainder.
- Common factors belong in the intersection.
- The greatest value in the intersection is the GCF.
GCF / LCM Venn Lab
Sort factors before calculating
Let the factors of 24 and 36 fall into a Venn diagram and discover their greatest shared factor.
What this game shows · GCF and LCM by Sorting
GCF (greatest common factor) and LCM (least common multiple) are easier when you sort factors instead of compute them. Drop the factor chips of two numbers into a Venn diagram — the intersection holds the common factors, and the biggest one is the GCF.
- Factor
- a number that divides another with no remainder.
- GCF
- greatest common factor — biggest number in the intersection.
- LCM
- least common multiple — product of all primes in the union (with max powers).
Aligned with CCSS 6.NS.B.4 (greatest common factor and least common multiple).
GCF / LCM factor sort
Common factors move into the intersection before any formula appears.
GCF 12
24 only824
common1234612
36 only91836
LCM = 72
Number theory explorer
Who this demo helps, and where to practice next
GCF / LCM Venn Lab is built for students who need factors, primes, composites, GCF, and LCM as visible structure. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
GCF / LCM Venn Lab helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
How to play
- 1 Sort or eliminate numbers by factor structure.
- 2 Explain why a number belongs in the prime, composite, shared, or multiple group.
- 3 Use the related topic pages for CCSS-aligned factor and GCF practice.
Continue with guided practice
FAQ
Tap to expand GCF and LCM, sorted.
01 What is the GCF of 24 and 36? 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common: 1, 2, 3, 4, 6, 12. GCF = 12.
02 What is the LCM of 24 and 36? 72
Prime factorizations: 24 = 2³ · 3, 36 = 2² · 3². LCM takes the highest power of each prime: 2³ · 3² = 8 · 9 = 72.
03 Why does GCF · LCM = product of the two numbers? GCF · LCM = a · b
Because every prime power either lands in the GCF (the min) or extends to the LCM (the max), and min + max = sum. So GCF × LCM = a × b. For 24 × 36 = 864 = 12 × 72.
04 Which grade is this game for? Grade 6
Grade 6, aligned with CCSS 6.NS.B.4. Foundation for fraction operations and modular arithmetic.