LCM of Three Numbers Worksheets - Free Printable

Let's solve each of these Least Common Multiple (LCM) problems step by step.

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What is LCM?

The Least Common Multiple (LCM) of a set of numbers is the smallest positive number that is divisible by all the numbers in the set.

We'll use prime factorization to find the LCM:
- Break each number into its prime factors.
- Take the highest power of each prime that appears.
- Multiply them together.

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1) LCM(8, 17, 2)

Prime factorizations:
- 8 = $2^3$
- 17 = $17^1$ (prime)
- 2 = $2^1$

Take the highest powers:
- $2^3$, $17^1$

LCM = $2^3 \times 17 = 8 \times 17 = \boxed{136}$

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2) LCM(22, 8, 4)

Factorize:
- 22 = $2 \times 11$
- 8 = $2^3$
- 4 = $2^2$

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

LCM = $2^3 \times 11 = 8 \times 11 = \boxed{88}$

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3) LCM(12, 36, 72)

Factorize:
- 12 = $2^2 \times 3$
- 36 = $2^2 \times 3^2$
- 72 = $2^3 \times 3^2$

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

LCM = $8 \times 9 = \boxed{72}$

> Note: 72 is divisible by all three numbers → LCM is 72.

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4) LCM(3, 37, 15)

Factorize:
- 3 = $3^1$
- 37 = $37^1$ (prime)
- 15 = $3 \times 5$

Highest powers:
- $3^1$, $5^1$, $37^1$

LCM = $3 \times 5 \times 37 = 15 \times 37 = \boxed{555}$

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5) LCM(5, 4, 10)

Factorize:
- 5 = $5^1$
- 4 = $2^2$
- 10 = $2 \times 5$

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

LCM = $4 \times 5 = \boxed{20}$

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6) LCM(18, 45, 90)

Factorize:
- 18 = $2 \times 3^2$
- 45 = $3^2 \times 5$
- 90 = $2 \times 3^2 \times 5$

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

LCM = $2 \times 9 \times 5 = \boxed{90}$

> 90 is divisible by all → LCM = 90

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7) LCM(42, 21, 34)

Factorize:
- 42 = $2 \times 3 \times 7$
- 21 = $3 \times 7$
- 34 = $2 \times 17$

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

LCM = $2 \times 3 \times 7 \times 17 = 6 \times 7 = 42; 42 \times 17 = \boxed{714}$

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8) LCM(50, 20, 40)

Factorize:
- 50 = $2 \times 5^2$
- 20 = $2^2 \times 5$
- 40 = $2^3 \times 5$

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

LCM = $8 \times 25 = \boxed{200}$

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9) LCM(56, 14, 8)

Factorize:
- 56 = $2^3 \times 7$
- 14 = $2 \times 7$
- 8 = $2^3$

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

LCM = $8 \times 7 = \boxed{56}$

> 56 is divisible by all → LCM = 56

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10) LCM(33, 12, 3)

Factorize:
- 33 = $3 \times 11$
- 12 = $2^2 \times 3$
- 3 = $3^1$

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

LCM = $4 \times 3 \times 11 = 12 \times 11 = \boxed{132}$

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✔ Final Answers:

1) LCM(8, 17, 2) = 136
2) LCM(22, 8, 4) = 88
3) LCM(12, 36, 72) = 72
4) LCM(3, 37, 15) = 555
5) LCM(5, 4, 10) = 20
6) LCM(18, 45, 90) = 90
7) LCM(42, 21, 34) = 714
8) LCM(50, 20, 40) = 200
9) LCM(56, 14, 8) = 56
10) LCM(33, 12, 3) = 132

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Let me know if you'd like this explained using the listing method or GCF method too!