Find the least common multiple (LCM) for each set of numbers on this math worksheet.
Worksheet titled "Least Common Multiple" with 10 problems to find the LCM of number sets, from 15Worksheets.com.
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Step-by-step solution for: Least Common Multiples Worksheets - 15 Worksheets Library
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Show Answer Key & Explanations
Step-by-step solution for: Least Common Multiples Worksheets - 15 Worksheets Library
Let’s solve each problem step by step to find the Least Common Multiple (LCM) for each set of numbers.
The LCM is the smallest number that all the given numbers can divide into evenly.
We’ll go one by one:
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1. 20, 10, 30
Multiples of 20: 20, 40, 60, 80...
Multiples of 10: 10, 20, 30, 40, 50, 60...
Multiples of 30: 30, 60, 90...
→ Smallest common multiple = 60
---
2. 15, 25, 30
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150...
Multiples of 25: 25, 50, 75, 100, 125, 150...
Multiples of 30: 30, 60, 90, 120, 150...
→ Smallest common multiple = 150
---
3. 12, 36, 20
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180...
Multiples of 36: 36, 72, 108, 144, 180...
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180...
→ Smallest common multiple = 180
---
4. 25, 40, 30
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600...
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600...
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600...
→ Smallest common multiple = 600
*(Alternatively, use prime factorization — but since we’re keeping it simple, listing multiples works here.)*
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5. 25, 20, 15
Multiples of 25: 25, 50, 75, 100, 125, 150...
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300...
Wait — let’s check smaller ones:
Try 300? Too big.
Check 150:
25 × 6 = 150 ✔
20 × 7.5 → not whole ✘
So no.
Try 300:
25 × 12 = 300 ✔
20 × 15 = 300 ✔
15 × 20 = 300 ✔
But maybe there’s a smaller one?
Try 60:
25 doesn’t divide 60 ✘
Try 100: 15 doesn’t divide 100 ✘
Try 150: 20 doesn’t divide 150 ✘
Try 300: works.
Actually, let’s do prime factors quickly to be sure:
25 = 5²
20 = 2² × 5
15 = 3 × 5
LCM = take highest powers: 2² × 3 × 5² = 4 × 3 × 25 = 300
→ So LCM = 300
---
6. 36, 12, 45
Prime factors:
36 = 2² × 3²
12 = 2² × 3
45 = 3² × 5
LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180
Check:
36 × 5 = 180 ✔
12 × 15 = 180 ✔
45 × 4 = 180 ✔
→ LCM = 180
---
7. 24, 9, 15
Prime factors:
24 = 2³ × 3
9 = 3²
15 = 3 × 5
LCM = 2³ × 3² × 5 = 8 × 9 × 5 = 360
Check:
24 × 15 = 360 ✔
9 × 40 = 360 ✔
15 × 24 = 360 ✔
→ LCM = 360
---
8. 20, 10, 15
Multiples:
20: 20, 40, 60...
10: 10, 20, 30, 40, 50, 60...
15: 15, 30, 45, 60...
→ All meet at 60
→ LCM = 60
---
9. 24, 36, 12
Note: 12 divides both 24 and 36, so LCM will be LCM of 24 and 36.
24 = 2³ × 3
36 = 2² × 3²
LCM = 2³ × 3² = 8 × 9 = 72
Check:
24 × 3 = 72 ✔
36 × 2 = 72 ✔
12 × 6 = 72 ✔
→ LCM = 72
---
10. 45, 25, 50
Prime factors:
45 = 3² × 5
25 = 5²
50 = 2 × 5²
LCM = 2 × 3² × 5² = 2 × 9 × 25 = 450
Check:
45 × 10 = 450 ✔
25 × 18 = 450 ✔
50 × 9 = 450 ✔
→ LCM = 450
---
Final Answer:
1. 60
2. 150
3. 180
4. 600
5. 300
6. 180
7. 360
8. 60
9. 72
10. 450
The LCM is the smallest number that all the given numbers can divide into evenly.
We’ll go one by one:
---
1. 20, 10, 30
Multiples of 20: 20, 40, 60, 80...
Multiples of 10: 10, 20, 30, 40, 50, 60...
Multiples of 30: 30, 60, 90...
→ Smallest common multiple = 60
---
2. 15, 25, 30
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150...
Multiples of 25: 25, 50, 75, 100, 125, 150...
Multiples of 30: 30, 60, 90, 120, 150...
→ Smallest common multiple = 150
---
3. 12, 36, 20
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180...
Multiples of 36: 36, 72, 108, 144, 180...
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180...
→ Smallest common multiple = 180
---
4. 25, 40, 30
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600...
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600...
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600...
→ Smallest common multiple = 600
*(Alternatively, use prime factorization — but since we’re keeping it simple, listing multiples works here.)*
---
5. 25, 20, 15
Multiples of 25: 25, 50, 75, 100, 125, 150...
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300...
Wait — let’s check smaller ones:
Try 300? Too big.
Check 150:
25 × 6 = 150 ✔
20 × 7.5 → not whole ✘
So no.
Try 300:
25 × 12 = 300 ✔
20 × 15 = 300 ✔
15 × 20 = 300 ✔
But maybe there’s a smaller one?
Try 60:
25 doesn’t divide 60 ✘
Try 100: 15 doesn’t divide 100 ✘
Try 150: 20 doesn’t divide 150 ✘
Try 300: works.
Actually, let’s do prime factors quickly to be sure:
25 = 5²
20 = 2² × 5
15 = 3 × 5
LCM = take highest powers: 2² × 3 × 5² = 4 × 3 × 25 = 300
→ So LCM = 300
---
6. 36, 12, 45
Prime factors:
36 = 2² × 3²
12 = 2² × 3
45 = 3² × 5
LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180
Check:
36 × 5 = 180 ✔
12 × 15 = 180 ✔
45 × 4 = 180 ✔
→ LCM = 180
---
7. 24, 9, 15
Prime factors:
24 = 2³ × 3
9 = 3²
15 = 3 × 5
LCM = 2³ × 3² × 5 = 8 × 9 × 5 = 360
Check:
24 × 15 = 360 ✔
9 × 40 = 360 ✔
15 × 24 = 360 ✔
→ LCM = 360
---
8. 20, 10, 15
Multiples:
20: 20, 40, 60...
10: 10, 20, 30, 40, 50, 60...
15: 15, 30, 45, 60...
→ All meet at 60
→ LCM = 60
---
9. 24, 36, 12
Note: 12 divides both 24 and 36, so LCM will be LCM of 24 and 36.
24 = 2³ × 3
36 = 2² × 3²
LCM = 2³ × 3² = 8 × 9 = 72
Check:
24 × 3 = 72 ✔
36 × 2 = 72 ✔
12 × 6 = 72 ✔
→ LCM = 72
---
10. 45, 25, 50
Prime factors:
45 = 3² × 5
25 = 5²
50 = 2 × 5²
LCM = 2 × 3² × 5² = 2 × 9 × 25 = 450
Check:
45 × 10 = 450 ✔
25 × 18 = 450 ✔
50 × 9 = 450 ✔
→ LCM = 450
---
Final Answer:
1. 60
2. 150
3. 180
4. 600
5. 300
6. 180
7. 360
8. 60
9. 72
10. 450
Parent Tip: Review the logic above to help your child master the concept of least common multiple practice worksheet.
