Explanation:
We need to find the
Least Common Multiple (LCM) of three numbers in each problem.
The LCM is the smallest number that all three numbers divide into evenly.
A reliable way to find LCM of three numbers is:
1. Find LCM of the first two numbers.
2. Then find LCM of that result and the third number.
We can use prime factorization or step-by-step division. Let’s do each one carefully.
---
1) 8, 17, 2
- Prime factors:
- 8 = 2³
- 17 = 17 (prime)
- 2 = 2¹
LCM takes highest power of each prime: 2³ × 17 = 8 × 17 =
136
✔ Check:
136 ÷ 8 = 17 ✔
136 ÷ 17 = 8 ✔
136 ÷ 2 = 68 ✔
Answer:
136
---
2) 22, 8, 4
- 22 = 2 × 11
- 8 = 2³
- 4 = 2²
Highest powers: 2³ × 11 = 8 × 11 =
88
✔ Check:
88 ÷ 22 = 4 ✔
88 ÷ 8 = 11 ✔
88 ÷ 4 = 22 ✔
Answer:
88
---
3) 12, 36, 72
Notice: 12 divides 36 (36 = 3×12), and 36 divides 72 (72 = 2×36). So the largest number, 72, is divisible by both others.
Check:
72 ÷ 12 = 6 ✔
72 ÷ 36 = 2 ✔
72 ÷ 72 = 1 ✔
So LCM =
72
---
4) 3, 37, 15
- 3 = 3
- 37 = 37 (prime)
- 15 = 3 × 5
Primes involved: 3, 5, 37
Highest powers: 3¹ × 5¹ × 37 = 3 × 5 × 37 = 15 × 37 =
555
✔ Check:
555 ÷ 3 = 185 ✔
555 ÷ 37 = 15 ✔
555 ÷ 15 = 37 ✔
Answer:
555
---
5) 5, 4, 10
- 5 = 5
- 4 = 2²
- 10 = 2 × 5
Primes: 2² and 5¹ → LCM = 4 × 5 =
20
✔ Check:
20 ÷ 5 = 4 ✔
20 ÷ 4 = 5 ✔
20 ÷ 10 = 2 ✔
Answer:
20
---
6) 18, 45, 90
Let’s factor:
- 18 = 2 × 3²
- 45 = 3² × 5
- 90 = 2 × 3² × 5
Highest powers: 2¹ × 3² × 5¹ = 2 × 9 × 5 =
90
Also, 90 is divisible by 18 (90 ÷ 18 = 5) and 45 (90 ÷ 45 = 2), so yes — LCM =
90
---
7) 42, 21, 34
Factor:
- 42 = 2 × 3 × 7
- 21 = 3 × 7
- 34 = 2 × 17
Primes: 2, 3, 7, 17
All appear once except none repeated beyond 1.
LCM = 2 × 3 × 7 × 17 = (2×3=6), (6×7=42), (42×17)
Compute 42 × 17:
40×17 = 680
2×17 = 34
Total = 680 + 34 =
714
✔ Check:
714 ÷ 42 = 17 ✔
714 ÷ 21 = 34 ✔
714 ÷ 34 = 21 ✔
Answer:
714
---
8) 50, 20, 40
Factor:
- 50 = 2 × 5²
- 20 = 2² × 5
- 40 = 2³ × 5
Highest powers: 2³ × 5² = 8 × 25 =
200
✔ Check:
200 ÷ 50 = 4 ✔
200 ÷ 20 = 10 ✔
200 ÷ 40 = 5 ✔
Answer:
200
---
9) 56, 14, 8
Factor:
- 56 = 2³ × 7
- 14 = 2 × 7
- 8 = 2³
Highest powers: 2³ × 7 = 8 × 7 =
56
Check:
56 ÷ 56 = 1 ✔
56 ÷ 14 = 4 ✔
56 ÷ 8 = 7 ✔
Answer:
56
---
10) 33, 12, 3
Factor:
- 33 = 3 × 11
- 12 = 2² × 3
- 3 = 3
Primes: 2², 3, 11 → LCM = 4 × 3 × 11 = 12 × 11 =
132
✔ Check:
132 ÷ 33 = 4 ✔
132 ÷ 12 = 11 ✔
132 ÷ 3 = 44 ✔
Answer:
132
Now let’s list all answers clearly:
1) 136
2) 88
3) 72
4) 555
5) 20
6) 90
7) 714
8) 200
9) 56
10) 132
Final Answer:
136, 88, 72, 555, 20, 90, 714, 200, 56, 132
Parent Tip: Review the logic above to help your child master the concept of lcm worksheet 5th grade.
