Math worksheet exploring the relationship between GCF and LCM with interactive table and educational illustration.

Let’s solve this step by step.

We are given pairs of numbers and need to fill in:
- Multiplication (just multiply the two numbers)
- GCF (Greatest Common Factor — the largest number that divides both)
- LCM (Least Common Multiple — the smallest number that both divide into)

Then we check if:
> LCM = Multiplication / GCF ?

This is actually a true math rule! So it should work for all pairs.

---

Let’s go row by row:

Row 1: 6, 7

- Multiplication: 6 × 7 = 42
- GCF: Factors of 6 → 1,2,3,6; Factors of 7 → 1,7 → only common factor is 1
- LCM: Since they’re coprime (GCF=1), LCM = 6×7 = 42
→ Check: 42 / 1 = 42 ✔

Row 2: 8, 9

- Multiplication: 8 × 9 = 72
- GCF: 8 → 1,2,4,8; 9 → 1,3,9 → only 1
- LCM: 8×9 = 72 (since GCF=1)
→ 72 / 1 = 72 ✔

Row 3: 4, 9

- Multiplication: 4 × 9 = 36
- GCF: 4 → 1,2,4; 9 → 1,3,9 → only 1
- LCM: 4×9 = 36
→ 36 / 1 = 36 ✔

Row 4: 5, 7

- Multiplication: 5 × 7 = 35
- GCF: both prime → 1
- LCM: 5×7 = 35
→ 35 / 1 = 35 ✔

Row 5: 6, 12

- Multiplication: 6 × 12 = 72
- GCF: factors of 6 → 1,2,3,6; 12 → 1,2,3,4,6,12 → greatest common is 6
- LCM: multiples of 6: 6,12,18...; 12: 12,24... → least common is 12
→ Check: 72 / 6 = 12 ✔

Row 6: 4, 16

- Multiplication: 4 × 16 = 64
- GCF: 4 → 1,2,4; 16 → 1,2,4,8,16 → greatest common is 4
- LCM: 16 is multiple of 4 → so LCM = 16
→ 64 / 4 = 16 ✔

Row 7: 10, 40

- Multiplication: 10 × 40 = 400
- GCF: 10 → 1,2,5,10; 40 → 1,2,4,5,8,10,20,40 → greatest common is 10
- LCM: 40 is multiple of 10 → LCM = 40
→ 400 / 10 = 40 ✔

Row 8: 7, 14

- Multiplication: 7 × 14 = 98
- GCF: 7 → 1,7; 14 → 1,2,7,14 → greatest common is 7
- LCM: 14 is multiple of 7 → LCM = 14
→ 98 / 7 = 14 ✔

Row 9: 6, 8

- Multiplication: 6 × 8 = 48
- GCF: 6 → 1,2,3,6; 8 → 1,2,4,8 → greatest common is 2
- LCM: multiples of 6: 6,12,18,24...; 8: 8,16,24... → LCM = 24
→ 48 / 2 = 24 ✔

Row 10: 8, 12

- Multiplication: 8 × 12 = 96
- GCF: 8 → 1,2,4,8; 12 → 1,2,3,4,6,12 → greatest common is 4
- LCM: multiples of 8: 8,16,24...; 12: 12,24... → LCM = 24
→ 96 / 4 = 24 ✔

Row 11: 10, 15

- Multiplication: 10 × 15 = 150
- GCF: 10 → 1,2,5,10; 15 → 1,3,5,15 → greatest common is 5
- LCM: multiples of 10: 10,20,30...; 15: 15,30... → LCM = 30
→ 150 / 5 = 30 ✔

Row 12: 12, 18

- Multiplication: 12 × 18 = 216
- GCF: 12 → 1,2,3,4,6,12; 18 → 1,2,3,6,9,18 → greatest common is 6
- LCM: multiples of 12: 12,24,36...; 18: 18,36... → LCM = 36
→ 216 / 6 = 36 ✔

---

Now, let’s fill the table with our answers:

| The numbers | Multiplication | GCF | LCM |
|-------------|----------------|-----|-----|
| 6, 7 | 42 | 1 | 42 |
| 8, 9 | 72 | 1 | 72 |
| 4, 9 | 36 | 1 | 36 |
| 5, 7 | 35 | 1 | 35 |
| 6, 12 | 72 | 6 | 12 |
| 4, 16 | 64 | 4 | 16 |
| 10, 40 | 400 | 10 | 40 |
| 7, 14 | 98 | 7 | 14 |
| 6, 8 | 48 | 2 | 24 |
| 8, 12 | 96 | 4 | 24 |
| 10, 15 | 150 | 5 | 30 |
| 12, 18 | 216 | 6 | 36 |

And yes — for every row, LCM = Multiplication ÷ GCF holds true.

Final Answer:
The completed table is as above, and yes, it is correct to say:
The LCM = Multiplication / GCF