Sure! Let’s solve each problem step by step and explain how to find the
first 2 common multiples of each number pair.
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🔢 What is a Common Multiple?
A
common multiple of two numbers is a number that is a multiple of
both numbers. We’re asked to list the
first two such numbers (usually starting from the smallest).
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##
✔ Problem 1: 5 and 6
Multiples of 5:
5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
5 × 5 = 25
5 × 6 = 30
5 × 7 = 35
5 × 8 = 40
5 × 9 = 45
5 × 10 = 50
5 × 11 = 55
5 × 12 = 60
→ So, multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
Multiples of 6:
6 × 1 = 6
6 × 2 = 12
6 × 3 = 18
6 × 4 = 24
6 × 5 = 30
6 × 6 = 36
6 × 7 = 42
6 × 8 = 48
6 × 9 = 54
6 × 10 = 60
→ Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
Common Multiples: Look for numbers that appear in both lists →
30, 60, ...
✔ First 2 common multiples:
30 and 60
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##
✔ Problem 2: 6 and 15
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, ...
Multiples of 15:
15, 30, 45, 60, 75, 90, 105, ...
Common Multiples: 30, 60, 90, ...
✔ First 2 common multiples:
30 and 60
*(Note: The LCM of 6 and 15 is 30, so all common multiples are multiples of 30.)*
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##
✔ Problem 3: 8 and 20
Multiples of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, ...
Multiples of 20:
20, 40, 60, 80, 100, 120, 140, ...
Common Multiples: 40, 80, 120, ...
✔ First 2 common multiples:
40 and 80
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##
✔ Problem 4: 6 and 10
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, ...
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, ...
Common Multiples: 30, 60, 90, 120, ...
✔ First 2 common multiples:
30 and 60
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## 📝 Final Answers to Fill In:
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5 and 6
- The multiples of 5 are:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
- The multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60
- The first 2 common multiples are:
30, 60
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6 and 15
- The multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60
- The multiples of 15 are:
15, 30, 45, 60, 75, 90
- The first 2 common multiples are:
30, 60
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8 and 20
- The multiples of 8 are:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80
- The multiples of 20 are:
20, 40, 60, 80, 100, 120
- The first 2 common multiples are:
40, 80
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6 and 10
- The multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60
- The multiples of 10 are:
10, 20, 30, 40, 50, 60, 70, 80
- The first 2 common multiples are:
30, 60
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## 💡 Tip:
You can also find the
Least Common Multiple (LCM) first, then multiply it by 1, 2, 3… to get common multiples.
Example: LCM(5,6) = 30 → First 2 common multiples: 30×1=30, 30×2=60.
This method is faster once you know how to compute LCM!
Let me know if you’d like help finding LCMs too 😊
Parent Tip: Review the logic above to help your child master the concept of common multiples worksheet.
