Least Common Multiple (LCM) worksheet for Grade 6 students to practice finding the LCM of three numbers.

Let's solve the Least Common Multiple (LCM) problems from the worksheet step by step. The goal is to find the LCM of three numbers for each problem.

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🔍 What is LCM?

The Least Common Multiple (LCM) of a set of numbers is the smallest number that is divisible by all of them.

We'll use prime factorization to find the LCM:
1. Break down each number into its prime factors.
2. Take the highest power of each prime that appears in any factorization.
3. Multiply those together to get the LCM.

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Let’s go through each problem:

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1) 14, 21, 7

- 14 = 2 × 7
- 21 = 3 × 7
- 7 = 7

Primes involved: 2, 3, 7
Highest powers: 2¹, 3¹, 7¹
→ LCM = 2 × 3 × 7 = 42

✔ Answer: 42

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2) 8, 19, 23

- 8 = 2³
- 19 = 19
- 23 = 23

All are primes or powers of primes.
→ LCM = 2³ × 19 × 23 = 8 × 19 × 23
Calculate:
8 × 19 = 152
152 × 23 = 3496

✔ Answer: 3496

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3) 13, 29, 21

- 13 = 13
- 29 = 29
- 21 = 3 × 7

All distinct primes → LCM = 13 × 29 × 3 × 7
Calculate:
13 × 29 = 377
3 × 7 = 21
377 × 21 = 7917

✔ Answer: 7917

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4) 19, 14, 8

- 19 = 19
- 14 = 2 × 7
- 8 = 2³

Primes: 2³, 7, 19
→ LCM = 2³ × 7 × 19 = 8 × 7 × 19
8 × 7 = 56
56 × 19 = 1064

✔ Answer: 1064

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5) 14, 28, 21

- 14 = 2 × 7
- 28 = 2² × 7
- 21 = 3 × 7

Primes: 2², 3, 7
→ LCM = 2² × 3 × 7 = 4 × 3 × 7 = 84

✔ Answer: 84

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6) 18, 29, 21

- 18 = 2 × 3²
- 29 = 29
- 21 = 3 × 7

Primes: 2, 3², 7, 29
→ LCM = 2 × 3² × 7 × 29 = 2 × 9 × 7 × 29
2 × 9 = 18
18 × 7 = 126
126 × 29 = 3654

✔ Answer: 3654

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7) 24, 11, 14

- 24 = 2³ × 3
- 11 = 11
- 14 = 2 × 7

Primes: 2³, 3, 7, 11
→ LCM = 2³ × 3 × 7 × 11 = 8 × 3 × 7 × 11
8 × 3 = 24
24 × 7 = 168
168 × 11 = 1848

✔ Answer: 1848

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8) 17, 30, 11

- 17 = 17
- 30 = 2 × 3 × 5
- 11 = 11

Primes: 2, 3, 5, 11, 17
→ LCM = 2 × 3 × 5 × 11 × 17
Step-by-step:
2 × 3 = 6
6 × 5 = 30
30 × 11 = 330
330 × 17 = 5610

✔ Answer: 5610

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9) 27, 23, 15

- 27 = 3³
- 23 = 23
- 15 = 3 × 5

Primes: 3³, 5, 23
→ LCM = 3³ × 5 × 23 = 27 × 5 × 23
27 × 5 = 135
135 × 23 = 3105

✔ Answer: 3105

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10) 21, 11, 15

- 21 = 3 × 7
- 11 = 11
- 15 = 3 × 5

Primes: 3, 5, 7, 11
→ LCM = 3 × 5 × 7 × 11 = 15 × 7 × 11
15 × 7 = 105
105 × 11 = 1155

✔ Answer: 1155

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11) 24, 14, 28

- 24 = 2³ × 3
- 14 = 2 × 7
- 28 = 2² × 7

Primes: 2³, 3, 7
→ LCM = 2³ × 3 × 7 = 8 × 3 × 7 = 168

✔ Answer: 168

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12) 3, 10, 14

- 3 = 3
- 10 = 2 × 5
- 14 = 2 × 7

Primes: 2, 3, 5, 7
→ LCM = 2 × 3 × 5 × 7 = 210

✔ Answer: 210

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13) 9, 13, 26

- 9 = 3²
- 13 = 13
- 26 = 2 × 13

Primes: 2, 3², 13
→ LCM = 2 × 3² × 13 = 2 × 9 × 13 = 18 × 13 = 234

✔ Answer: 234

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14) 9, 27, 2

- 9 = 3²
- 27 = 3³
- 2 = 2

Primes: 2, 3³
→ LCM = 2 × 3³ = 2 × 27 = 54

✔ Answer: 54

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15) 23, 13, 15

- 23 = 23
- 13 = 13
- 15 = 3 × 5

All distinct primes → LCM = 23 × 13 × 3 × 5
23 × 13 = 299
3 × 5 = 15
299 × 15 = 4485

✔ Answer: 4485

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16) 14, 17, 12

- 14 = 2 × 7
- 17 = 17
- 12 = 2² × 3

Primes: 2², 3, 7, 17
→ LCM = 2² × 3 × 7 × 17 = 4 × 3 × 7 × 17
4 × 3 = 12
12 × 7 = 84
84 × 17 = 1428

✔ Answer: 1428

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## ✔ Final Answers:

| Problem | Numbers | LCM |
|--------|--------|-----|
| 1 | 14, 21, 7 | 42 |
| 2 | 8, 19, 23 | 3496 |
| 3 | 13, 29, 21 | 7917 |
| 4 | 19, 14, 8 | 1064 |
| 5 | 14, 28, 21 | 84 |
| 6 | 18, 29, 21 | 3654 |
| 7 | 24, 11, 14 | 1848 |
| 8 | 17, 30, 11 | 5610 |
| 9 | 27, 23, 15 | 3105 |
| 10 | 21, 11, 15 | 1155 |
| 11 | 24, 14, 28 | 168 |
| 12 | 3, 10, 14 | 210 |
| 13 | 9, 13, 26 | 234 |
| 14 | 9, 27, 2 | 54 |
| 15 | 23, 13, 15 | 4485 |
| 16 | 14, 17, 12 | 1428 |

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Let me know if you'd like a printable version or explanations using another method (like listing multiples).