Grade 6 Math Worksheet - Least common multiple (LCM) of 3 numbers ... - Free Printable
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Step-by-step solution for: Grade 6 Math Worksheet - Least common multiple (LCM) of 3 numbers ...
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Step-by-step solution for: Grade 6 Math Worksheet - Least common multiple (LCM) of 3 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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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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- 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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- 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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- 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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- 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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- 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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- 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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- 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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- 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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- 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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- 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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- 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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- 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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- 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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- 9 = 3²
- 27 = 3³
- 2 = 2
Primes: 2, 3³
→ LCM = 2 × 3³ = 2 × 27 = 54
✔ Answer: 54
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- 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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- 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 explanation with visual factor trees!
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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.
---
Let’s go through each problem:
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
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 explanation with visual factor trees!
Parent Tip: Review the logic above to help your child master the concept of lcm worksheet with answers.
