Fun math activity worksheet where students solve GCF and LCM problems to crack a code and reveal a joke about polar bears.

I'll solve this GCF and LCM worksheet step by step, calculating each value carefully.

Let me work through all the problems:

GCF Section:

1. B: GCF of 60 and 75
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 75: 1, 3, 5, 15, 25, 75
- Common factors: 1, 3, 5, 15
- GCF = 15

2. R: GCF of 28 and 70
- Factors of 28: 1, 2, 4, 7, 14, 28
- Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
- Common factors: 1, 2, 7, 14
- GCF = 14

3. K: GCF of 16 and 50
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 50: 1, 2, 5, 10, 25, 50
- Common factors: 1, 2
- GCF = 2

4. F: GCF of 75 and 92
- Factors of 75: 1, 3, 5, 15, 25, 75
- Factors of 92: 1, 2, 4, 23, 46, 92
- Common factors: 1
- GCF = 1

5. O: GCF of 49 and 84
- Factors of 49: 1, 7, 49
- Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Common factors: 1, 7
- GCF = 7

6. H: GCF of 32 and 40
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Common factors: 1, 2, 4, 8
- GCF = 8

7. G: GCF of 88 (only one number given - this seems incomplete, but let me check if it's paired with something)
Looking at the pattern, it appears to be GCF of two numbers. Let me re-examine... It looks like it might be 88 and another number that's cut off or it's a single number exercise. I'll assume it needs clarification, but based on typical worksheets, let me check if there's a pattern. Actually, looking more carefully at the layout, I need to find what pairs with 88.

Let me reconsider the layout - it appears each box has two numbers. For G, I see "88" but need the other number. Let me proceed with what's visible and note any issues.

Actually, looking at the structure again, I believe G should have two numbers. Let me assume standard pairing and continue with LCM section first, then return.

LCM Section:

1. T: LCM of 12 and 15
- Multiples of 12: 12, 24, 36, 48, 60, 72...
- Multiples of 15: 15, 30, 45, 60, 75...
- LCM = 60

2. N: LCM of 6 and 14
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48...
- Multiples of 14: 14, 28, 42, 56...
- LCM = 42

3. I: LCM of 6 and 9
- Multiples of 6: 6, 12, 18, 24...
- Multiples of 9: 9, 18, 27...
- LCM = 18

4. P: LCM of 10 and 5
- Multiples of 10: 10, 20, 30...
- Multiples of 5: 5, 10, 15, 20...
- LCM = 10

5. A: LCM of 10 and 11
- Since 10 and 11 are coprime (no common factors except 1)
- LCM = 10 × 11 = 110

6. E: LCM of 4 and 11
- Since 4 and 11 are coprime
- LCM = 4 × 11 = 44

7. V: LCM of 5 and 9
- Since 5 and 9 are coprime
- LCM = 5 × 9 = 45

8. S: LCM of 10 and 20
- Multiples of 10: 10, 20, 30...
- Multiples of 20: 20, 40...
- LCM = 20

Now let me go back to G. Looking at the pattern in the worksheet, I notice G appears to have only "88" visible. However, checking typical worksheet patterns and the code at the bottom, let me see what makes sense.

Looking at the code line at the bottom: 56, 42, 75, 10, 1, 100, 42, 10, 1, 18, 44, 2, 2

Wait, I need to match my answers to these codes. Let me list what I have:

GCF answers:
- B = 15
- R = 14
- K = 2
- F = 1
- O = 7
- H = 8
- G = ? (need second number)

LCM answers:
- T = 60
- N = 42
- I = 18
- P = 10
- A = 110
- E = 44
- V = 45
- S = 20

Looking at the code: 56, 42, 75, 10, 1, 100, 42, 10, 1, 18, 44, 2, 2

I see some matches:
- 42 appears (matches N)
- 10 appears twice (matches P)
- 1 appears twice (matches F)
- 18 appears (matches I)
- 44 appears (matches E)
- 2 appears twice (matches K)

For G, since I can only see "88", let me think about what would pair with it to give a GCF that's in the code. The remaining codes are: 56, 75, 100

If GCF involves 88:
- 88 = 2³ × 11
- For GCF to be 56 = 2³ × 7, we'd need a multiple of 56 that shares factors with 88
- For GCF to be 75 = 3 × 5², doesn't work with 88
- For GCF to be 100 = 2² × 5², doesn't work well with 88

Actually, looking more carefully at the image layout, I realize G might be paired with another number I'm not seeing clearly. Let me assume it's a standard problem and the answer should fit the code.

Given the code values and that most of my answers match, let me assume G needs to produce one of: 56, 75, or 100.

Since 88 = 2³ × 11, for a GCF to work:
- If the other number is 56 = 2³ × 7, then GCF(88, 56) = 2³ = 8 (but H already = 8)
- This doesn't seem right...

Let me reconsider. Perhaps I misread the layout. Let me just provide the answers I'm confident about and note that G may need clarification.

Actually, wait - looking at the joke at the bottom "Where do polar bears store their money?" - the answer letters should spell out something. Let me see what letters correspond to which positions in the code.

The code has 13 numbers, and I have 13 letter boxes (B, R, K, F, O, H, G, T, N, I, P, A, E, V, S - that's 15 actually).

Let me recount the boxes more carefully from the image description:
GCF: B, R, K, F, O, H, G (7 boxes)
LCM: T, N, I, P, A, E, V, S (8 boxes)
Total: 15 boxes

But the code has 13 numbers. This suggests some answers might repeat or I'm miscounting.

Let me just provide my calculated answers: