Here are the solutions for each pair of numbers. I have calculated the Least Common Multiple (LCM) and the Greatest Common Factor (GCF) for each row.
1. Pair: 16, 10
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LCM: The multiples of 16 are 16, 32, 48, 64, 80... The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80... The first number they share is
80.
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GCF: The factors of 16 are 1, 2, 4, 8, 16. The factors of 10 are 1, 2, 5, 10. The largest factor they share is
2.
2. Pair: 14, 6
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LCM: Multiples of 14: 14, 28, 42... Multiples of 6: 6, 12, 18, 24, 30, 36, 42... The first match is
42.
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GCF: Factors of 14: 1, 2, 7, 14. Factors of 6: 1, 2, 3, 6. The largest shared factor is
2.
3. Pair: 3, 27
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LCM: Since 27 is a multiple of 3 ($3 \times 9 = 27$), the LCM is just the larger number,
27.
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GCF: Since 3 goes evenly into 27, the greatest common factor is the smaller number,
3.
4. Pair: 6, 14
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LCM: Multiples of 14: 14, 28, 42... Multiples of 6: 6, 12, 18, 24, 30, 36, 42... The first match is
42.
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GCF: Factors of 6: 1, 2, 3, 6. Factors of 14: 1, 2, 7, 14. The largest shared factor is
2.
5. Pair: 16, 5
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LCM: These numbers share no common factors other than 1. So, you just multiply them: $16 \times 5 = $
80.
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GCF: The only factor they share is
1.
6. Pair: 8, 12
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LCM: Multiples of 8: 8, 16, 24... Multiples of 12: 12, 24... The first match is
24.
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GCF: Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. The largest shared factor is
4.
7. Pair: 16, 6
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LCM: Multiples of 16: 16, 32, 48... Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48... The first match is
48.
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GCF: Factors of 16: 1, 2, 4, 8, 16. Factors of 6: 1, 2, 3, 6. The largest shared factor is
2.
8. Pair: 8, 3
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LCM: These numbers share no common factors other than 1. Multiply them: $8 \times 3 = $
24.
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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 common multiple worksheet.
