Least Common Multiple Worksheets | Download Free Printables For Kids - Free Printable

Explanation:
We need to find the Least Common Multiple (LCM) of three numbers in each problem.
The LCM is the smallest number that all three numbers divide into evenly.

A reliable way for small numbers is:
1. Prime factorize each number.
2. For each prime, take the highest power that appears in any factorization.
3. Multiply those together.

Let’s go through each one carefully.

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① 9, 27, 2

- 9 = 3²
- 27 = 3³
- 2 = 2¹

Primes involved: 2 and 3
Highest powers: 2¹, 3³
→ LCM = 2 × 27 = 54

✔ Check:
54 ÷ 9 = 6 ✔
54 ÷ 27 = 2 ✔
54 ÷ 2 = 27 ✔

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② 14, 17, 12

- 14 = 2 × 7
- 17 = 17 (prime)
- 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)+(4×17) = 1360 + 68 = 1428

✔ Check divisibility:
1428 ÷ 14 = 102 ✔
1428 ÷ 17 = 84 ✔
1428 ÷ 12 = 119 ✔

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③ 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
56 × 20 = 1120 → minus 56 = 1064

✔ Check:
1064 ÷ 19 = 56 ✔
1064 ÷ 14 = 76 ✔
1064 ÷ 8 = 133 ✔

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④ 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 × 77 =
24 × 70 = 1680, 24 × 7 = 168 → total = 1848

✔ Check:
1848 ÷ 24 = 77 ✔
1848 ÷ 11 = 168 ✔
1848 ÷ 14 = 132 ✔

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⑤ 3, 10, 14

- 3 = 3
- 10 = 2 × 5
- 14 = 2 × 7

Primes: 2, 3, 5, 7
Highest powers: 2¹, 3¹, 5¹, 7¹
→ LCM = 2 × 3 × 5 × 7 = 6 × 35 = 210

✔ Check:
210 ÷ 3 = 70 ✔
210 ÷ 10 = 21 ✔
210 ÷ 14 = 15 ✔

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⑥ 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

✔ Check:
84 ÷ 14 = 6 ✔
84 ÷ 28 = 3 ✔
84 ÷ 21 = 4 ✔

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⑦ 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 =
10×13=130, 8×13=104 → 130+104 = 234

✔ Check:
234 ÷ 9 = 26 ✔
234 ÷ 13 = 18 ✔
234 ÷ 26 = 9 ✔

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⑧ 13, 29, 21

- 13 = 13
- 29 = 29
- 21 = 3 × 7

All primes are distinct: 3, 7, 13, 29
→ LCM = 3 × 7 × 13 × 29
First: 3 × 7 = 21
21 × 13 = 273
273 × 29:
273 × 30 = 8190 → minus 273 = 7917

✔ Check:
7917 ÷ 13 = 609 ✔
7917 ÷ 29 = 273 ✔
7917 ÷ 21 = 377 ✔ (21 × 377 = 7917)

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⑨ 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

✔ Check:
3654 ÷ 18 = 203 ✔
3654 ÷ 29 = 126 ✔
3654 ÷ 21 = 174 ✔ (21×174 = 3654)

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⑩ 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

✔ Check:
3105 ÷ 27 = 115 ✔
3105 ÷ 23 = 135 ✔
3105 ÷ 15 = 207 ✔

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Now list all answers in order:

1. 54
2. 1428
3. 1064
4. 1848
5. 210
6. 84
7. 234
8. 7917
9. 3654
10. 3105

Final Answer:
54, 1428, 1064, 1848, 210, 84, 234, 7917, 3654, 3105