Grade 5 Factoring Worksheets: Lowest Common Multiple (LCM) | Worsheets library - Free Printable

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 these together to get the LCM.

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Now, 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 primes are distinct:
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 primes: 3, 7, 13, 29
LCM = 3 × 7 × 13 × 29
= 21 × 13 = 273
273 × 29 = 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
= 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
= 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 = 8 × 3 × 7 × 11 = 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
= 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 = 27 × 5 × 23 = 135 × 23
= 135 × 20 + 135 × 3 = 2700 + 405 = 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 = 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 = 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 × 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 × 27 = 54

✔ Answer: 54

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15) 23, 13, 15

- 23 = 23
- 13 = 13
- 15 = 3 × 5

Primes: 3, 5, 13, 23
LCM = 3 × 5 × 13 × 23
= 15 × 13 = 195; 195 × 23 = 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 = 4 × 3 × 7 × 17 = 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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📌 Tips for Students:

- Always factor each number into primes.
- Use exponents for repeated primes.
- Take the highest exponent for each prime.
- Multiply all those together.

Let me know if you'd like this as a printable answer key or with steps shown in a table!