Grade 6 Math Worksheet - Least common multiple (LCM) of 3 numbers ... - Free Printable
Educational worksheet: Grade 6 Math Worksheet - Least common multiple (LCM) of 3 numbers .... Download and print for classroom or home learning activities.
GIF
359×464
9.3 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1464153
⭐
Show Answer Key & Explanations
Step-by-step solution for: Grade 6 Math Worksheet - Least common multiple (LCM) of 3 numbers ...
▼
Show Answer Key & Explanations
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.
---
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.
---
Now, let’s go through each problem:
---
- 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
---
- 8 = 2³
- 19 = 19 (prime)
- 23 = 23 (prime)
All are distinct primes or powers:
LCM = 2³ × 19 × 23 = 8 × 19 × 23
Calculate:
8 × 19 = 152
152 × 23 = 3496
✔ Answer: 3496
---
- 13 = 13
- 29 = 29
- 21 = 3 × 7
All are distinct primes:
LCM = 13 × 29 × 3 × 7
Step-by-step:
13 × 29 = 377
3 × 7 = 21
377 × 21 = 7917
✔ Answer: 7917
---
- 19 = 19
- 14 = 2 × 7
- 8 = 2³
Primes: 2, 7, 19
Highest powers:
- 2³, 7¹, 19¹
LCM = 8 × 7 × 19 = 56 × 19 = 1064
✔ Answer: 1064
---
- 14 = 2 × 7
- 28 = 2² × 7
- 21 = 3 × 7
Primes: 2, 3, 7
Highest powers:
- 2², 3¹, 7¹
LCM = 4 × 3 × 7 = 84
✔ Answer: 84
---
- 18 = 2 × 3²
- 29 = 29
- 21 = 3 × 7
Primes: 2, 3, 7, 29
Highest powers:
- 2¹, 3², 7¹, 29¹
LCM = 2 × 9 × 7 × 29 = 18 × 7 = 126; 126 × 29
126 × 30 = 3780 → minus 126 = 3654
✔ Answer: 3654
---
- 24 = 2³ × 3
- 11 = 11
- 14 = 2 × 7
Primes: 2, 3, 7, 11
Highest powers:
- 2³, 3¹, 7¹, 11¹
LCM = 8 × 3 × 7 × 11 = 24 × 7 = 168; 168 × 11 = 1848
✔ Answer: 1848
---
- 17 = 17
- 30 = 2 × 3 × 5
- 11 = 11
Primes: 2, 3, 5, 11, 17
All appear once
LCM = 2 × 3 × 5 × 11 × 17
Step-by-step:
2×3=6; 6×5=30; 30×11=330; 330×17 = ?
330 × 10 = 3300
330 × 7 = 2310
Total = 3300 + 2310 = 5610
✔ Answer: 5610
---
- 27 = 3³
- 23 = 23
- 15 = 3 × 5
Primes: 3, 5, 23
Highest powers:
- 3³, 5¹, 23¹
LCM = 27 × 5 × 23 = 135 × 23
135 × 20 = 2700; 135 × 3 = 405 → total = 3105
✔ Answer: 3105
---
- 21 = 3 × 7
- 11 = 11
- 15 = 3 × 5
Primes: 3, 5, 7, 11
Highest powers:
- 3¹, 5¹, 7¹, 11¹
LCM = 3 × 5 × 7 × 11 = 15 × 7 = 105; 105 × 11 = 1155
✔ Answer: 1155
---
- 24 = 2³ × 3
- 14 = 2 × 7
- 28 = 2² × 7
Primes: 2, 3, 7
Highest powers:
- 2³, 3¹, 7¹
LCM = 8 × 3 × 7 = 168
✔ Answer: 168
---
- 3 = 3
- 10 = 2 × 5
- 14 = 2 × 7
Primes: 2, 3, 5, 7
All appear once
LCM = 2 × 3 × 5 × 7 = 210
✔ Answer: 210
---
- 9 = 3²
- 13 = 13
- 26 = 2 × 13
Primes: 2, 3, 13
Highest powers:
- 2¹, 3², 13¹
LCM = 2 × 9 × 13 = 18 × 13 = 234
✔ Answer: 234
---
- 9 = 3²
- 27 = 3³
- 2 = 2
Primes: 2, 3
Highest powers:
- 2¹, 3³
LCM = 2 × 27 = 54
✔ Answer: 54
---
- 23 = 23
- 13 = 13
- 15 = 3 × 5
All distinct primes:
LCM = 23 × 13 × 3 × 5
Step-by-step:
23 × 13 = 299
3 × 5 = 15
299 × 15 = ?
300 × 15 = 4500 → subtract 1 × 15 = 15 → 4500 - 15 = 4485
✔ Answer: 4485
---
- 14 = 2 × 7
- 17 = 17
- 12 = 2² × 3
Primes: 2, 3, 7, 17
Highest powers:
- 2², 3¹, 7¹, 17¹
LCM = 4 × 3 × 7 × 17 = 12 × 7 = 84; 84 × 17 = ?
80 × 17 = 1360
4 × 17 = 68
Total = 1360 + 68 = 1428
✔ Answer: 1428
---
| 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 |
---
Let me know if you'd like a printable version or explanation for any specific problem!
---
🔍 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.
---
Now, 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 (prime)
- 23 = 23 (prime)
All are distinct primes or powers:
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 are distinct primes:
LCM = 13 × 29 × 3 × 7
Step-by-step:
13 × 29 = 377
3 × 7 = 21
377 × 21 = 7917
✔ Answer: 7917
---
4) 19, 14, 8
- 19 = 19
- 14 = 2 × 7
- 8 = 2³
Primes: 2, 7, 19
Highest powers:
- 2³, 7¹, 19¹
LCM = 8 × 7 × 19 = 56 × 19 = 1064
✔ Answer: 1064
---
5) 14, 28, 21
- 14 = 2 × 7
- 28 = 2² × 7
- 21 = 3 × 7
Primes: 2, 3, 7
Highest powers:
- 2², 3¹, 7¹
LCM = 4 × 3 × 7 = 84
✔ Answer: 84
---
6) 18, 29, 21
- 18 = 2 × 3²
- 29 = 29
- 21 = 3 × 7
Primes: 2, 3, 7, 29
Highest powers:
- 2¹, 3², 7¹, 29¹
LCM = 2 × 9 × 7 × 29 = 18 × 7 = 126; 126 × 29
126 × 30 = 3780 → minus 126 = 3654
✔ Answer: 3654
---
7) 24, 11, 14
- 24 = 2³ × 3
- 11 = 11
- 14 = 2 × 7
Primes: 2, 3, 7, 11
Highest powers:
- 2³, 3¹, 7¹, 11¹
LCM = 8 × 3 × 7 × 11 = 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
All appear once
LCM = 2 × 3 × 5 × 11 × 17
Step-by-step:
2×3=6; 6×5=30; 30×11=330; 330×17 = ?
330 × 10 = 3300
330 × 7 = 2310
Total = 3300 + 2310 = 5610
✔ Answer: 5610
---
9) 27, 23, 15
- 27 = 3³
- 23 = 23
- 15 = 3 × 5
Primes: 3, 5, 23
Highest powers:
- 3³, 5¹, 23¹
LCM = 27 × 5 × 23 = 135 × 23
135 × 20 = 2700; 135 × 3 = 405 → total = 3105
✔ Answer: 3105
---
10) 21, 11, 15
- 21 = 3 × 7
- 11 = 11
- 15 = 3 × 5
Primes: 3, 5, 7, 11
Highest powers:
- 3¹, 5¹, 7¹, 11¹
LCM = 3 × 5 × 7 × 11 = 15 × 7 = 105; 105 × 11 = 1155
✔ Answer: 1155
---
11) 24, 14, 28
- 24 = 2³ × 3
- 14 = 2 × 7
- 28 = 2² × 7
Primes: 2, 3, 7
Highest powers:
- 2³, 3¹, 7¹
LCM = 8 × 3 × 7 = 168
✔ Answer: 168
---
12) 3, 10, 14
- 3 = 3
- 10 = 2 × 5
- 14 = 2 × 7
Primes: 2, 3, 5, 7
All appear once
LCM = 2 × 3 × 5 × 7 = 210
✔ Answer: 210
---
13) 9, 13, 26
- 9 = 3²
- 13 = 13
- 26 = 2 × 13
Primes: 2, 3, 13
Highest powers:
- 2¹, 3², 13¹
LCM = 2 × 9 × 13 = 18 × 13 = 234
✔ Answer: 234
---
14) 9, 27, 2
- 9 = 3²
- 27 = 3³
- 2 = 2
Primes: 2, 3
Highest powers:
- 2¹, 3³
LCM = 2 × 27 = 54
✔ Answer: 54
---
15) 23, 13, 15
- 23 = 23
- 13 = 13
- 15 = 3 × 5
All distinct primes:
LCM = 23 × 13 × 3 × 5
Step-by-step:
23 × 13 = 299
3 × 5 = 15
299 × 15 = ?
300 × 15 = 4500 → subtract 1 × 15 = 15 → 4500 - 15 = 4485
✔ Answer: 4485
---
16) 14, 17, 12
- 14 = 2 × 7
- 17 = 17
- 12 = 2² × 3
Primes: 2, 3, 7, 17
Highest powers:
- 2², 3¹, 7¹, 17¹
LCM = 4 × 3 × 7 × 17 = 12 × 7 = 84; 84 × 17 = ?
80 × 17 = 1360
4 × 17 = 68
Total = 1360 + 68 = 1428
✔ Answer: 1428
---
✔ 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 |
---
Let me know if you'd like a printable version or explanation for any specific problem!
Parent Tip: Review the logic above to help your child master the concept of common multiple worksheet.
