🔢 Step 1: Choose Your Numbers

Enter two positive integers (for example, 12 and 18). Press Start to begin the breakdown process. Each stage pauses briefly so you can see how the numbers unfold and relate.

🧱 Step 2: Break into Prime Pieces

Watch as each number is divided step by step into its prime factors. Each prime appears as a separate colored tile, falling neatly into place beneath the original number. For instance, 12 will show 2 × 2 × 3, while 18 becomes 2 × 3 × 3. The motion is simple and slow enough to follow — every split is an action you can see.

🎨 Step 3: Match and Multiply

When both numbers are factorized, the game highlights shared primes using matching colors. These shared tiles combine to form the GCD. Then the system gathers all primes — both shared and unique — to build the LCM. Each multiplication step is shown visually: tiles merge and grow into the final numbers.

🔁 Step 4: Compare and Replay

After both results appear, the display shows a quick summary:

• GCD – made from shared factors.
• LCM – made from all factors combined.

Try new number pairs to see how different factorizations lead to new patterns. Notice how numbers with many shared primes have small LCMs, while those with few shared primes grow larger.

🧠 Numbers as Building Blocks

Every number can be broken down into a unique combination of prime factors — like a structure made from Lego bricks. In this game, those bricks are made visible. Seeing how two numbers share or differ in their bricks provides an intuitive foundation for understanding divisibility, multiples, and number relationships.

🤝 GCD and LCM: Two Sides of the Same Relationship

The Greatest Common Divisor (GCD) is built from the primes both numbers share. It represents the largest number that can divide both without remainder. In contrast, the Least Common Multiple (LCM) is constructed from all primes found in either number, using the highest power of each. It represents the smallest number that both original numbers divide into exactly.

🌈 Visual Patterns to Notice

• Numbers that share many factors (like 12 and 18) have a large GCD and a relatively small LCM.
• Numbers that share few or no factors (like 8 and 15) have a small GCD and a large LCM.
• When one number divides the other (like 6 and 18), the smaller number itself is the GCD, and the larger is the LCM.

💬 Discussion Prompts

Use the visuals to start number stories or real-world analogies:

• “If two kids are jumping rope in rhythms of 6 and 8 beats, when will they land together again?”
• “If two clocks chime every 9 and 12 minutes, when do they ring at the same time?”

Relating the abstract patterns to everyday timing or motion helps learners connect GCD and LCM to shared cycles and repetition in real life.

📘 For Teachers and Curious Minds

The demonstration can be paused and replayed to emphasize reasoning steps. Teachers can use it to explain how factorization connects division and multiplication, or to show that LCM × GCD = Product of the two numbers — a neat numerical symmetry that always holds true. Encouraging students to predict outcomes before each reveal builds both number sense and confidence.