Here are the solutions for the Least Common Multiple (LCM) and Greatest Common Factor (GCF) problems.
1. Numbers: 16, 10
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LCM: Multiples of 16 are 16, 32, 48, 64,
80. Multiples of 10 are 10, 20...
80. The LCM is
80.
*
GCF: Factors of 16 are 1, 2, 4, 8, 16. Factors of 10 are 1, 2, 5, 10. The largest shared factor is
2.
2. Numbers: 14, 6
*
LCM: Multiples of 14 are 14, 28,
42. Multiples of 6 are 6, 12...
42. The LCM is
42.
*
GCF: Factors of 14 are 1, 2, 7, 14. Factors of 6 are 1, 2, 3, 6. The largest shared factor is
2.
3. Numbers: 3, 27
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LCM: Since 27 is a multiple of 3 ($3 \times 9 = 27$), the LCM is
27.
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GCF: Since 3 goes evenly into 27, the GCF is
3.
4. Numbers: 6, 14
*
LCM: Multiples of 14 are 14, 28,
42. Multiples of 6 go 6, 12...
42. The LCM is
42.
*
GCF: Factors of 6 are 1, 2, 3, 6. Factors of 14 are 1, 2, 7, 14. The largest shared factor is
2.
5. Numbers: 16, 5
*
LCM: These numbers share no common factors other than 1. Multiply them: $16 \times 5 = $
80.
*
GCF: The only factor they share is
1.
6. Numbers: 8, 12
*
LCM: Multiples of 12 are 12,
24. Multiples of 8 are 8, 16,
24. The LCM is
24.
*
GCF: Factors of 8 are 1, 2, 4, 8. Factors of 12 are 1, 2, 3, 4, 6, 12. The largest shared factor is
4.
7. Numbers: 16, 6
*
LCM: Multiples of 16 are 16, 32,
48. Multiples of 6 go 6, 12...
48. The LCM is
48.
*
GCF: Factors of 16 are 1, 2, 4, 8, 16. Factors of 6 are 1, 2, 3, 6. The largest shared factor is
2.
8. Numbers: 8, 3
*
LCM: These numbers share no common factors other than 1. Multiply them: $8 \times 3 = $
24.
*
GCF: The only factor they share is
1.
Final Answer:
16, 10: LCM: 80, GCF: 2
14, 6: LCM: 42, GCF: 2
3, 27: LCM: 27, GCF: 3
6, 14: LCM: 42, GCF: 2
16, 5: LCM: 80, GCF: 1
8, 12: LCM: 24, GCF: 4
16, 6: LCM: 48, GCF: 2
8, 3: LCM: 24, GCF: 1
Parent Tip: Review the logic above to help your child master the concept of finding the gcf worksheet.
