Let's solve each of the LCM (Least Common Multiple) problems step by step.
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🔍 Understanding LCM:
The
LCM of two numbers is the
smallest number that is a multiple of both numbers.
💡
Shortcut Rule:
If one number is a
multiple of the other, then the
LCM = the greater number.
For example:
- 6 and 12 → 12 is a multiple of 6 → LCM = 12
We’ll use this rule where applicable.
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Now let’s go through each problem:
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a) 3 and 24
- Is 24 a multiple of 3? Yes (3 × 8 = 24)
→ So, LCM =
24
✔ LCM = 24
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b) 5 and 25
- Is 25 a multiple of 5? Yes (5 × 5 = 25)
→ So, LCM =
25
✔ LCM = 25
---
c) 15 and 60
- Is 60 a multiple of 15? Yes (15 × 4 = 60)
→ So, LCM =
60
✔ LCM = 60
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d) 16 and 48
- Is 48 a multiple of 16? Yes (16 × 3 = 48)
→ So, LCM =
48
✔ LCM = 48
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e) 7 and 42
- Is 42 a multiple of 7? Yes (7 × 6 = 42)
→ So, LCM =
42
✔ LCM = 42
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f) 18 and 36
- Is 36 a multiple of 18? Yes (18 × 2 = 36)
→ So, LCM =
36
✔ LCM = 36
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g) 36 and 72
- Is 72 a multiple of 36? Yes (36 × 2 = 72)
→ So, LCM =
72
✔ LCM = 72
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h) 9 and 81
- Is 81 a multiple of 9? Yes (9 × 9 = 81)
→ So, LCM =
81
✔ LCM = 81
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i) 20 and 40
- Is 40 a multiple of 20? Yes (20 × 2 = 40)
→ So, LCM =
40
✔ LCM = 40
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j) 25 and 50
- Is 50 a multiple of 25? Yes (25 × 2 = 50)
→ So, LCM =
50
✔ LCM = 50
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k) 8 and 72
- Is 72 a multiple of 8? Yes (8 × 9 = 72)
→ So, LCM =
72
✔ LCM = 72
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l) 19 and 95
- Is 95 a multiple of 19? Let's check:
19 × 5 = 95 → Yes!
→ So, LCM =
95
✔ LCM = 95
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m) 16 and 64
- Is 64 a multiple of 16? Yes (16 × 4 = 64)
→ So, LCM =
64
✔ LCM = 64
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n) 45 and 90
- Is 90 a multiple of 45? Yes (45 × 2 = 90)
→ So, LCM =
90
✔ LCM = 90
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✔ Final Answers:
| Problem | LCM |
|--------|-----|
| a) 3 and 24 |
24 |
| b) 5 and 25 |
25 |
| c) 15 and 60 |
60 |
| d) 16 and 48 |
48 |
| e) 7 and 42 |
42 |
| f) 18 and 36 |
36 |
| g) 36 and 72 |
72 |
| h) 9 and 81 |
81 |
| i) 20 and 40 |
40 |
| j) 25 and 50 |
50 |
| k) 8 and 72 |
72 |
| l) 19 and 95 |
95 |
| m) 16 and 64 |
64 |
| n) 45 and 90 |
90 |
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🎯 Summary:
All these pairs have one number as a
multiple of the other. Therefore, in every case, the
LCM is the greater number.
This makes solving them very fast!
Let me know if you'd like to see how to find LCM using prime factorization for more complex cases!
Parent Tip: Review the logic above to help your child master the concept of lcm worksheets.
