LCM Worksheet for Grade 5 students to practice finding the least common multiple of number pairs.

Let's solve each problem step by step to find the Least Common Multiple (LCM) of the given pairs of numbers.

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🔹 What is LCM?

The LCM of two numbers is the smallest number that is a multiple of both numbers.

We can find the LCM using:
- Listing multiples, or
- Prime factorization

We'll use prime factorization for efficiency.

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✔ a) 4 and 24

- Prime factors of 4: $ 2^2 $
- Prime factors of 24: $ 2^3 \times 3 $
- Take the highest powers: $ 2^3 \times 3 = 8 \times 3 = 24 $

✔ LCM = 24

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✔ b) 20 and 40

- 20 = $ 2^2 \times 5 $
- 40 = $ 2^3 \times 5 $
- Highest powers: $ 2^3 \times 5 = 8 \times 5 = 40 $

✔ LCM = 40

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✔ c) 5 and 15

- 5 = $ 5 $
- 15 = $ 3 \times 5 $
- Highest powers: $ 3 \times 5 = 15 $

✔ LCM = 15

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✔ d) 2 and 12

- 2 = $ 2 $
- 12 = $ 2^2 \times 3 $
- Highest powers: $ 2^2 \times 3 = 4 \times 3 = 12 $

✔ LCM = 12

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✔ e) 4 and 14

- 4 = $ 2^2 $
- 14 = $ 2 \times 7 $
- Highest powers: $ 2^2 \times 7 = 4 \times 7 = 28 $

✔ LCM = 28

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✔ f) 3 and 8

- 3 = $ 3 $
- 8 = $ 2^3 $
- No common factors → multiply: $ 3 \times 8 = 24 $

✔ LCM = 24

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✔ g) 4 and 18

- 4 = $ 2^2 $
- 18 = $ 2 \times 3^2 $
- Highest powers: $ 2^2 \times 3^2 = 4 \times 9 = 36 $

✔ LCM = 36

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✔ h) 6 and 8

- 6 = $ 2 \times 3 $
- 8 = $ 2^3 $
- Highest powers: $ 2^3 \times 3 = 8 \times 3 = 24 $

✔ LCM = 24

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✔ i) 3 and 16

- 3 = $ 3 $
- 16 = $ 2^4 $
- No common factors → $ 3 \times 16 = 48 $

✔ LCM = 48

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✔ j) 5 and 24

- 5 = $ 5 $
- 24 = $ 2^3 \times 3 $
- No common factors → $ 5 \times 24 = 120 $

✔ LCM = 120

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📝 Final Answers:

a) 4 and 24 = 24
b) 20 and 40 = 40
c) 5 and 15 = 15
d) 2 and 12 = 12
e) 4 and 14 = 28
f) 3 and 8 = 24
g) 4 and 18 = 36
h) 6 and 8 = 24
i) 3 and 16 = 48
j) 5 and 24 = 120

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Let me know if you'd like this explained in another way (like listing multiples)!