Of course! Let's solve each problem on the "Least Common Multiple" worksheet step by step.
The
Least Common Multiple (LCM) of two numbers is the smallest positive number that is a multiple of both numbers.
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Problem 1: LCM of 20 and 25
Prime factorization:
- 20 = 2² × 5
- 25 = 5²
LCM = highest power of all primes = 2² × 5² = 4 × 25 = 100
✔ Correct answer:
b) 100
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Problem 2: LCM of 40 and 60
Prime factorization:
- 40 = 2³ × 5
- 60 = 2² × 3 × 5
LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120
✔ Correct answer:
d) 120
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Problem 3: LCM of 30 and 60
Since 60 is a multiple of 30 (60 ÷ 30 = 2), the LCM is the larger number.
✔ Correct answer:
a) 60
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Problem 4: LCM of 28 and 42
Prime factorization:
- 28 = 2² × 7
- 42 = 2 × 3 × 7
LCM = 2² × 3 × 7 = 4 × 3 × 7 = 84
✔ Correct answer:
a) 84
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Problem 5: LCM of 24 and 60
Prime factorization:
- 24 = 2³ × 3
- 60 = 2² × 3 × 5
LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120
✔ Correct answer:
a) 120
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Problem 6: LCM of 50 and 75
Prime factorization:
- 50 = 2 × 5²
- 75 = 3 × 5²
LCM = 2 × 3 × 5² = 2 × 3 × 25 = 150
✔ Correct answer:
d) 150
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Problem 7: LCM of 80 and 100
Prime factorization:
- 80 = 2⁴ × 5
- 100 = 2² × 5²
LCM = 2⁴ × 5² = 16 × 25 = 400
✔ Correct answer:
c) 400
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Problem 8: LCM of 90 and 60
Prime factorization:
- 90 = 2 × 3² × 5
- 60 = 2² × 3 × 5
LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180
✔ Correct answer:
b) 180
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✔ Final Answers:
1.
b) 100
2.
d) 120
3.
a) 60
4.
a) 84
5.
a) 120
6.
d) 150
7.
c) 400
8.
b) 180
You can circle these answers on your worksheet! Let me know if you’d like to see another method (like listing multiples) for any of them.
Parent Tip: Review the logic above to help your child master the concept of least common multiple worksheet and answers.
