Class 6 Maths worksheet on LCM and GCF with numerical problems and word problems.

Let's solve the problems step by step.

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Part 1: Find LCM and GCF of the given pairs

We will find both the Least Common Multiple (LCM) and Greatest Common Factor (GCF) for each pair.

#### Method Recap:
- GCF: The largest number that divides both numbers.
- LCM: The smallest number that is a multiple of both numbers.
- Use prime factorization or listing multiples/factors.

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1. (6, 30)

- Factors of 6: 1, 2, 3, 6
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- GCF = 6
- Multiples of 6: 6, 12, 18, 24, 30, ...
- Multiples of 30: 30, 60, ...
- LCM = 30

✔ (6, 30): GCF = 6, LCM = 30

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2. (18, 12)

- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 12: 1, 2, 3, 4, 6, 12
- GCF = 6
- Multiples of 18: 18, 36, 54, ...
- Multiples of 12: 12, 24, 36, ...
- LCM = 36

✔ (18, 12): GCF = 6, LCM = 36

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3. (21, 18)

- Factors of 21: 1, 3, 7, 21
- Factors of 18: 1, 2, 3, 6, 9, 18
- GCF = 3
- Multiples of 21: 21, 42, 63, 84, 105, 126, ...
- Multiples of 18: 18, 36, 54, 72, 90, 108, 126, ...
- LCM = 126

✔ (21, 18): GCF = 3, LCM = 126

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4. (24, 15)

- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 15: 1, 3, 5, 15
- GCF = 3
- Multiples of 24: 24, 48, 72, 96, 120, ...
- Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
- LCM = 120

✔ (24, 15): GCF = 3, LCM = 120

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5. (16, 22)

- Factors of 16: 1, 2, 4, 8, 16
- Factors of 22: 1, 2, 11, 22
- GCF = 2
- Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, ...
- Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, ...
- LCM = 176

✔ (16, 22): GCF = 2, LCM = 176

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6. (14, 21)

- Factors of 14: 1, 2, 7, 14
- Factors of 21: 1, 3, 7, 21
- GCF = 7
- Multiples of 14: 14, 28, 42, 56, ...
- Multiples of 21: 21, 42, 63, ...
- LCM = 42

✔ (14, 21): GCF = 7, LCM = 42

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7. (25, 10)

- Factors of 25: 1, 5, 25
- Factors of 10: 1, 2, 5, 10
- GCF = 5
- Multiples of 25: 25, 50, 75, ...
- Multiples of 10: 10, 20, 30, 40, 50, ...
- LCM = 50

✔ (25, 10): GCF = 5, LCM = 50

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8. (12, 3)

- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 3: 1, 3
- GCF = 3
- Multiples of 12: 12, 24, 36, ...
- Multiples of 3: 3, 6, 9, 12, 15, ...
- LCM = 12

✔ (12, 3): GCF = 3, LCM = 12

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9. (10, 14)

- Factors of 10: 1, 2, 5, 10
- Factors of 14: 1, 2, 7, 14
- GCF = 2
- Multiples of 10: 10, 20, 30, 40, 50, 60, 70, ...
- Multiples of 14: 14, 28, 42, 56, 70, ...
- LCM = 70

✔ (10, 14): GCF = 2, LCM = 70

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10. (28, 2)

- Factors of 28: 1, 2, 4, 7, 14, 28
- Factors of 2: 1, 2
- GCF = 2
- Multiples of 28: 28, 56, ...
- Multiples of 2: 2, 4, 6, ..., 28, ...
- LCM = 28

✔ (28, 2): GCF = 2, LCM = 28

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11. (12, 8)

- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 8: 1, 2, 4, 8
- GCF = 4
- Multiples of 12: 12, 24, 36, ...
- Multiples of 8: 8, 16, 24, ...
- LCM = 24

✔ (12, 8): GCF = 4, LCM = 24

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12. (4, 28)

- Factors of 4: 1, 2, 4
- Factors of 28: 1, 2, 4, 7, 14, 28
- GCF = 4
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
- Multiples of 28: 28, 56, ...
- LCM = 28

✔ (4, 28): GCF = 4, LCM = 28

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13. (48, 24)

- Since 24 divides 48 evenly:
- GCF = 24
- LCM = 48

✔ (48, 24): GCF = 24, LCM = 48

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14. (6, 12)

- 6 divides 12 → GCF = 6, LCM = 12

✔ (6, 12): GCF = 6, LCM = 12

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15. (40, 25)

- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 25: 1, 5, 25
- GCF = 5
- Multiples of 40: 40, 80, 120, 160, 200, ...
- Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, ...
- LCM = 200

✔ (40, 25): GCF = 5, LCM = 200

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16. (26, 16)

- Factors of 26: 1, 2, 13, 26
- Factors of 16: 1, 2, 4, 8, 16
- GCF = 2
- Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260, 286, 312, ...
- Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, ...
- LCM = 208

✔ (26, 16): GCF = 2, LCM = 208

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17. (14, 30)

- Factors of 14: 1, 2, 7, 14
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- GCF = 2
- Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, ...
- Multiples of 30: 30, 60, 90, 120, 150, 180, 210, ...
- LCM = 210

✔ (14, 30): GCF = 2, LCM = 210

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18. (14, 48)

- Factors of 14: 1, 2, 7, 14
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- GCF = 2
- Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, ...
- Multiples of 48: 48, 96, 144, 192, 240, 288, 336, ...
- LCM = 336

✔ (14, 48): GCF = 2, LCM = 336

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## ✔ Summary Table:

| Pair | GCF | LCM |
|------|-----|-----|
| (6,30) | 6 | 30 |
| (18,12) | 6 | 36 |
| (21,18) | 3 | 126 |
| (24,15) | 3 | 120 |
| (16,22) | 2 | 176 |
| (14,21) | 7 | 42 |
| (25,10) | 5 | 50 |
| (12,3) | 3 | 12 |
| (10,14) | 2 | 70 |
| (28,2) | 2 | 28 |
| (12,8) | 4 | 24 |
| (4,28) | 4 | 28 |
| (48,24) | 24 | 48 |
| (6,12) | 6 | 12 |
| (40,25) | 5 | 200 |
| (26,16) | 2 | 208 |
| (14,30) | 2 | 210 |
| (14,48) | 2 | 336 |

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## 🔍 Word Problems

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1. Ishann's Trail Mix

He has:
- 18 bags of peanuts
- 9 bags of almonds

He wants to make identical portions with no leftovers.

👉 This is a GCF problem — we need the greatest number of portions such that each portion has same number of peanut and almond bags.

So, GCF of 18 and 9:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 9: 1, 3, 9
- GCF = 9

So, he can make 9 portions, each with:
- 18 ÷ 9 = 2 bags of peanuts
- 9 ÷ 9 = 1 bag of almonds

✔ Answer: 9 portions

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2. Traffic Lights Blinking

- One blinks every 4 seconds
- Other blinks every 6 seconds
- Both start at the same time
- How many times do they blink together in 60 seconds?

They blink together at the LCM of 4 and 6.

- LCM of 4 and 6:
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
- LCM = 12

So, they blink together every 12 seconds.

Now, how many times in 60 seconds?
- 60 ÷ 12 = 5

But include the start (at 0 seconds), so:
- Times: 0, 12, 24, 36, 48, 60 → that’s 6 times

Wait! But does "in 60 seconds" include t=60?

Yes — because it says “in 60 seconds”, meaning from t=0 to t=60.

So:
- At t = 0, 12, 24, 36, 48, 60 → 6 times

✔ Answer: 6 times

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3. Arvind's Cousins

Let:
- Number of cousin sisters = x
- Number of cousin brothers = x (same total)

Sisters take pictures in groups of 5 → so x must be divisible by 5
Brothers take pictures in groups of 10 → so x must be divisible by 10

So x must be a common multiple of 5 and 10.

But we want the minimum number of cousin sisters.

So find LCM of 5 and 10 → LCM = 10

So minimum x = 10

✔ Answer: 10

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## ✔ Final Answers:

Word Problems:

1. 9
2. 6
3. 10

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