Sure! Let’s solve this
Grade 5 Math Worksheet-2 on
LCM (Least Common Multiple) and
HCF (Highest Common Factor) step by step.
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PART I: FIND THE LCM OF THE FOLLOWING NUMBERS
We’ll use the
prime factorization method to find LCM.
>
LCM Rule: Take the
highest power of each prime factor appearing in any number.
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1. LCM of 16, 24, 40
Prime factorizations:
- 16 = 2⁴
- 24 = 2³ × 3
- 40 = 2³ × 5
→ Highest powers: 2⁴, 3¹, 5¹
→
LCM = 2⁴ × 3 × 5 = 16 × 3 × 5 = 240
✔ Answer: 240
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2. LCM of 72, 96, 120
Prime factorizations:
- 72 = 2³ × 3²
- 96 = 2⁵ × 3
- 120 = 2³ × 3 × 5
→ Highest powers: 2⁵, 3², 5¹
→
LCM = 2⁵ × 3² × 5 = 32 × 9 × 5 = 1440
✔ Answer: 1440
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3. LCM of 102, 170, 136
Prime factorizations:
- 102 = 2 × 3 × 17
- 170 = 2 × 5 × 17
- 136 = 2³ × 17
→ Highest powers: 2³, 3¹, 5¹, 17¹
→
LCM = 8 × 3 × 5 × 17 = 8 × 3 = 24; 24 × 5 = 120; 120 × 17 = 2040
✔ Answer: 2040
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4. LCM of 84, 144
Prime factorizations:
- 84 = 2² × 3 × 7
- 144 = 2⁴ × 3²
→ Highest powers: 2⁴, 3², 7¹
→
LCM = 16 × 9 × 7 = 144 × 7 = 1008
✔ Answer: 1008
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5. LCM of 120, 168
Prime factorizations:
- 120 = 2³ × 3 × 5
- 168 = 2³ × 3 × 7
→ Highest powers: 2³, 3¹, 5¹, 7¹
→
LCM = 8 × 3 × 5 × 7 = 8 × 3 = 24; 24 × 5 = 120; 120 × 7 = 840
✔ Answer: 840
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6. LCM of 120, 150, 135
Prime factorizations:
- 120 = 2³ × 3 × 5
- 150 = 2 × 3 × 5²
- 135 = 3³ × 5
→ Highest powers: 2³, 3³, 5²
→
LCM = 8 × 27 × 25
Let’s compute:
- 8 × 27 = 216
- 216 × 25 = 5400
✔ Answer: 5400
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PART II: FIND THE HCF USING FACTORISATION METHOD
>
HCF Rule: Take the
lowest power of common prime factors.
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1. HCF of 48, 56, 72
Prime factorizations:
- 48 = 2⁴ × 3
- 56 = 2³ × 7
- 72 = 2³ × 3²
→ Common prime factor: only
2, lowest power is
2³ = 8
✔ Answer: 8
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2. HCF of 102, 68, 136
Prime factorizations:
- 102 = 2 × 3 × 17
- 68 = 2² × 17
- 136 = 2³ × 17
→ Common primes:
2 and 17
→ Lowest powers: 2¹, 17¹ →
2 × 17 = 34
✔ Answer: 34
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3. HCF of 120, 168
Prime factorizations:
- 120 = 2³ × 3 × 5
- 168 = 2³ × 3 × 7
→ Common primes: 2³, 3¹ →
8 × 3 = 24
✔ Answer: 24
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4. HCF of 84, 144
Prime factorizations:
- 84 = 2² × 3 × 7
- 144 = 2⁴ × 3²
→ Common primes: 2², 3¹ →
4 × 3 = 12
✔ Answer: 12
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5. HCF of 198, 360
Prime factorizations:
- 198 = 2 × 3² × 11
- 360 = 2³ × 3² × 5
→ Common primes: 2¹, 3² →
2 × 9 = 18
✔ Answer: 18
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6. HCF of 44, 66, 110
Prime factorizations:
- 44 = 2² × 11
- 66 = 2 × 3 × 11
- 110 = 2 × 5 × 11
→ Common primes: 2¹, 11¹ →
2 × 11 = 22
✔ Answer: 22
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✔ FINAL ANSWERS:
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I. LCM Answers:
1.
240
2.
1440
3.
2040
4.
1008
5.
840
6.
5400
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II. HCF Answers (using factorisation):
1.
8
2.
34
3.
24
4.
12
5.
18
6.
22
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Parent Tip: Review the logic above to help your child master the concept of hcf worksheet.
