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

Let's solve each of these Least Common Multiple (LCM) problems step by step. The LCM of three numbers is the smallest number that is divisible by all three.

We'll use the prime factorization method for accuracy.

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🔢 Problem 1: 9, 27, 2

- Prime factors:
- 9 = $3^2$
- 27 = $3^3$
- 2 = $2^1$

- Take the highest power of each prime:
- $2^1$, $3^3$

- LCM = $2 \times 3^3 = 2 \times 27 = \boxed{54}$

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🔢 Problem 2: 14, 17, 12

- Prime factors:
- 14 = $2 \times 7$
- 17 = $17$ (prime)
- 12 = $2^2 \times 3$

- Highest powers:
- $2^2$, $3^1$, $7^1$, $17^1$

- LCM = $4 \times 3 \times 7 \times 17 = 12 \times 7 = 84; 84 \times 17 = \boxed{1428}$

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🔢 Problem 3: 19, 14, 8

- Prime factors:
- 19 = $19$ (prime)
- 14 = $2 \times 7$
- 8 = $2^3$

- Highest powers:
- $2^3$, $7^1$, $19^1$

- LCM = $8 \times 7 \times 19 = 56 \times 19 = \boxed{1064}$

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🔢 Problem 4: 24, 11, 14

- Prime factors:
- 24 = $2^3 \times 3$
- 11 = $11$
- 14 = $2 \times 7$

- Highest powers:
- $2^3$, $3^1$, $7^1$, $11^1$

- LCM = $8 \times 3 \times 7 \times 11 = 24 \times 7 = 168; 168 \times 11 = \boxed{1848}$

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🔢 Problem 5: 3, 10, 14

- Prime factors:
- 3 = $3$
- 10 = $2 \times 5$
- 14 = $2 \times 7$

- Highest powers:
- $2^1$, $3^1$, $5^1$, $7^1$

- LCM = $2 \times 3 \times 5 \times 7 = \boxed{210}$

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🔢 Problem 6: 14, 28, 21

- Prime factors:
- 14 = $2 \times 7$
- 28 = $2^2 \times 7$
- 21 = $3 \times 7$

- Highest powers:
- $2^2$, $3^1$, $7^1$

- LCM = $4 \times 3 \times 7 = 12 \times 7 = \boxed{84}$

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🔢 Problem 7: 9, 13, 26

- Prime factors:
- 9 = $3^2$
- 13 = $13$
- 26 = $2 \times 13$

- Highest powers:
- $2^1$, $3^2$, $13^1$

- LCM = $2 \times 9 \times 13 = 18 \times 13 = \boxed{234}$

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🔢 Problem 8: 13, 29, 21

- Prime factors:
- 13 = $13$
- 29 = $29$ (both prime)
- 21 = $3 \times 7$

- All primes: $3, 7, 13, 29$

- LCM = $3 \times 7 \times 13 \times 29$

Step-by-step:
- $3 \times 7 = 21$
- $21 \times 13 = 273$
- $273 \times 29 = ?$

Calculate:
- $273 \times 30 = 8190$
- Subtract $273$: $8190 - 273 = \boxed{7917}$

So, LCM = $\boxed{7917}$

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🔢 Problem 9: 18, 29, 21

- Prime factors:
- 18 = $2 \times 3^2$
- 29 = $29$
- 21 = $3 \times 7$

- Highest powers:
- $2^1$, $3^2$, $7^1$, $29^1$

- LCM = $2 \times 9 \times 7 \times 29$

Step-by-step:
- $2 \times 9 = 18$
- $18 \times 7 = 126$
- $126 \times 29 = ?$

Break it down:
- $126 \times 30 = 3780$
- Subtract $126$: $3780 - 126 = \boxed{3654}$

So, LCM = $\boxed{3654}$

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🔢 Problem 10: 27, 23, 15

- Prime factors:
- 27 = $3^3$
- 23 = $23$ (prime)
- 15 = $3 \times 5$

- Highest powers:
- $3^3$, $5^1$, $23^1$

- LCM = $27 \times 5 \times 23$

Step-by-step:
- $27 \times 5 = 135$
- $135 \times 23 = ?$

Break it down:
- $135 \times 20 = 2700$
- $135 \times 3 = 405$
- Total: $2700 + 405 = \boxed{3105}$

So, LCM = $\boxed{3105}$

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✔ Final Answers:

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

Let me know if you'd like a visual explanation or help with any specific one!