LCM GCF Class 6 Maths Worksheet | Class1to12.com - Free Printable

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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Solutions:

1. (6, 30)
- Factors:
6 = 2 × 3
30 = 2 × 3 × 5
- GCF = 2 × 3 = 6
- LCM = 2 × 3 × 5 = 30

2. (18, 12)
- 18 = 2 × 3²
12 = 2² × 3
- GCF = 2 × 3 = 6
- LCM = 2² × 3² = 4 × 9 = 36

3. (21, 18)
- 21 = 3 × 7
18 = 2 × 3²
- GCF = 3
- LCM = 2 × 3² × 7 = 2 × 9 × 7 = 126

4. (24, 15)
- 24 = 2³ × 3
15 = 3 × 5
- GCF = 3
- LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120

5. (16, 22)
- 16 = 2⁴
22 = 2 × 11
- GCF = 2
- LCM = 2⁴ × 11 = 16 × 11 = 176

6. (14, 21)
- 14 = 2 × 7
21 = 3 × 7
- GCF = 7
- LCM = 2 × 3 × 7 = 42

7. (25, 10)
- 25 = 5²
10 = 2 × 5
- GCF = 5
- LCM = 2 × 5² = 2 × 25 = 50

8. (12, 3)
- 12 = 2² × 3
3 = 3
- GCF = 3
- LCM = 2² × 3 = 4 × 3 = 12

9. (10, 14)
- 10 = 2 × 5
14 = 2 × 7
- GCF = 2
- LCM = 2 × 5 × 7 = 70

10. (28, 2)
- 28 = 2² × 7
2 = 2
- GCF = 2
- LCM = 2² × 7 = 4 × 7 = 28

11. (12, 8)
- 12 = 2² × 3
8 = 2³
- GCF = 2² = 4
- LCM = 2³ × 3 = 8 × 3 = 24

12. (4, 28)
- 4 = 2²
28 = 2² × 7
- GCF = 2² = 4
- LCM = 2² × 7 = 4 × 7 = 28

13. (48, 24)
- 48 = 2⁴ × 3
24 = 2³ × 3
- GCF = 2³ × 3 = 8 × 3 = 24
- LCM = 2⁴ × 3 = 16 × 3 = 48

14. (6, 12)
- 6 = 2 × 3
12 = 2² × 3
- GCF = 2 × 3 = 6
- LCM = 2² × 3 = 4 × 3 = 12

15. (40, 25)
- 40 = 2³ × 5
25 = 5²
- GCF = 5
- LCM = 2³ × 5² = 8 × 25 = 200

16. (26, 16)
- 26 = 2 × 13
16 = 2⁴
- GCF = 2
- LCM = 2⁴ × 13 = 16 × 13 = 208

17. (14, 30)
- 14 = 2 × 7
30 = 2 × 3 × 5
- GCF = 2
- LCM = 2 × 3 × 5 × 7 = 210

18. (14, 48)
- 14 = 2 × 7
48 = 2⁴ × 3
- GCF = 2
- LCM = 2⁴ × 3 × 7 = 16 × 3 × 7 = 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. Trail Mix Problem

> Ishann has 18 bags of peanuts and 9 bags of almonds. He wants to make identical portions with no leftovers. What is the greatest number of portions?

This is a GCF problem — we want the largest number that divides both 18 and 9 evenly.

- GCF of 18 and 9:
- 18 = 2 × 3²
- 9 = 3²
- GCF = 3² = 9

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

Answer: 9

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2. Traffic Lights Blinking

> One light blinks every 4 seconds, the other every 6 seconds. Both start at the same time. How many times do they blink together in 60 seconds?

They blink together at intervals equal to the LCM of 4 and 6.

- LCM of 4 and 6:
- 4 = 2²
- 6 = 2 × 3
- LCM = 2² × 3 = 12 seconds

So, they blink together every 12 seconds.

Now, in 60 seconds:
- Number of times = 60 ÷ 12 = 5 times

But wait — they blink at the same time at t = 0, then again at 12, 24, 36, 48, 60.

So:
- 0, 12, 24, 36, 48, 60 → that’s 6 times

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

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

So:
- At t = 0: first blink together
- Then every 12 seconds: 12, 24, 36, 48, 60 → total of 6 times

✔ Answer: 6

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3. Cousin Sisters and Brothers

> Arvind has the same number of cousin sisters and cousin brothers. Sisters take photos in groups of 5, uncles in groups of 10. What is the minimum number of cousin sisters?

Let the number of cousin sisters = number of cousin brothers = x

- Sisters are photographed in groups of 5 → so x must be divisible by 5
- Uncles (brothers) are photographed in groups of 10 → so x must be divisible by 10

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

We want the minimum such x → LCM of 5 and 10

- LCM(5, 10) = 10

✔ So, minimum number of cousin sisters = 10

Check:
- 10 sisters → can form 10 ÷ 5 = 2 groups
- 10 brothers → can form 10 ÷ 10 = 1 group
- Equal number → satisfies condition

Answer: 10

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## ✔ Final Answers:

LCM & GCF:

As shown in the table above.

Word Problems:

1. 9
2. 6
3. 10

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