Let's solve each of these
Least Common Multiple (LCM) problems step by step. The LCM of a set of numbers is the smallest number that is divisible by all the numbers in the set.
We’ll use
prime factorization or the
division method to find the LCM for each group.
---
1) LCM(8, 17, 2)
- Prime factors:
- 8 = 2³
- 17 = 17¹ (prime)
- 2 = 2¹
- Take the highest powers of all primes: 2³ × 17¹ = 8 × 17 =
136
✔ LCM = 136
---
2) LCM(22, 8, 4)
- Prime factors:
- 22 = 2 × 11
- 8 = 2³
- 4 = 2²
- Highest powers: 2³ × 11 = 8 × 11 =
88
✔ LCM = 88
---
3) LCM(12, 36, 72)
- Prime factors:
- 12 = 2² × 3
- 36 = 2² × 3²
- 72 = 2³ × 3²
- Highest powers: 2³ × 3² = 8 × 9 =
72
✔ LCM = 72
> Note: Since 72 is divisible by both 12 and 36, it’s the LCM.
---
4) LCM(3, 37, 15)
- Prime factors:
- 3 = 3¹
- 37 = 37¹ (prime)
- 15 = 3 × 5
- Highest powers: 3¹ × 5¹ × 37¹ = 3 × 5 × 37 = 15 × 37 =
555
✔ LCM = 555
---
5) LCM(5, 4, 10)
- Prime factors:
- 5 = 5
- 4 = 2²
- 10 = 2 × 5
- Highest powers: 2² × 5 = 4 × 5 =
20
✔ LCM = 20
---
6) LCM(18, 45, 90)
- Prime factors:
- 18 = 2 × 3²
- 45 = 3² × 5
- 90 = 2 × 3² × 5
- Highest powers: 2 × 3² × 5 = 2 × 9 × 5 =
90
✔ LCM = 90
> Note: 90 is divisible by all three.
---
7) LCM(42, 21, 34)
- Prime factors:
- 42 = 2 × 3 × 7
- 21 = 3 × 7
- 34 = 2 × 17
- All primes: 2, 3, 7, 17
- Highest powers: 2 × 3 × 7 × 17 = ?
Step-by-step:
- 2 × 3 = 6
- 6 × 7 = 42
- 42 × 17 = 714
✔ LCM = 714
---
8) LCM(50, 20, 40)
- Prime factors:
- 50 = 2 × 5²
- 20 = 2² × 5
- 40 = 2³ × 5
- Highest powers: 2³ × 5² = 8 × 25 =
200
✔ LCM = 200
---
9) LCM(56, 14, 8)
- Prime factors:
- 56 = 2³ × 7
- 14 = 2 × 7
- 8 = 2³
- Highest powers: 2³ × 7 = 8 × 7 =
56
✔ LCM = 56
> 56 is divisible by 14 and 8 → so yes!
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10) LCM(33, 12, 3)
- Prime factors:
- 33 = 3 × 11
- 12 = 2² × 3
- 3 = 3
- Highest powers: 2² × 3 × 11 = 4 × 3 × 11 = 12 × 11 =
132
✔ LCM = 132
---
✔ Final Answers:
1)
136
2)
88
3)
72
4)
555
5)
20
6)
90
7)
714
8)
200
9)
56
10)
132
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Let me know if you'd like a visual explanation or steps using the division method!
Parent Tip: Review the logic above to help your child master the concept of least common multiple worksheet 6th grade.
