Find the GCF and LCM af each set of number 1.12 and 24 2.16 and 24 3.12 and 16 4.9 and 12 5.20 and 25 6.15 and 35 7.24 and 40 8.36 and 60 9.8 and 12 10.27 and 36 please answer this

Find the GCF and LCM af each set of number 1.12 and 24 2.16 and 24 3.12 and 16 4.9 and 12 5.20 and 25 6.15 and 35 7.24 and 40 8.36 and 60 9.8 and 12 10.27 and 36 please answer this

The Correct Answer and Explanation is:

To find the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of two numbers, we need to follow these steps:

1. Find the Prime Factorizations

• Break down each number into its prime factors.

2. For GCF:

• The GCF is the product of all the prime factors that are common to both numbers, raised to the smallest power that appears in both factorizations.

3. For LCM:

• The LCM is the product of all prime factors from both numbers, raised to the largest power that appears in either factorization.

Let’s go through each pair of numbers:

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1. 12 and 24

• Prime Factorization of 12: 12 = 2² * 3
• Prime Factorization of 24: 24 = 2³ * 3

GCF: The common factors are 222²22 and 333, so GCF = 2² * 3 = 12.
LCM: The factors are 232³23 and 333, so LCM = 2³ * 3 = 24.

2. 16 and 24

• Prime Factorization of 16: 16 = 2⁴
• Prime Factorization of 24: 24 = 2³ * 3

GCF: The common factor is 232³23, so GCF = 2³ = 8.
LCM: The factors are 242⁴24 and 333, so LCM = 2⁴ * 3 = 48.

3. 12 and 16

• Prime Factorization of 12: 12 = 2² * 3
• Prime Factorization of 16: 16 = 2⁴

GCF: The common factor is 222²22, so GCF = 2² = 4.
LCM: The factors are 242⁴24 and 333, so LCM = 2⁴ * 3 = 48.

4. 9 and 12

• Prime Factorization of 9: 9 = 3²
• Prime Factorization of 12: 12 = 2² * 3

GCF: The common factor is 333, so GCF = 3.
LCM: The factors are 222²22 and 323²32, so LCM = 2² * 3² = 36.

5. 20 and 25

• Prime Factorization of 20: 20 = 2² * 5
• Prime Factorization of 25: 25 = 5²

GCF: The common factor is 555, so GCF = 5.
LCM: The factors are 222²22 and 525²52, so LCM = 2² * 5² = 100.

6. 15 and 35

• Prime Factorization of 15: 15 = 3 * 5
• Prime Factorization of 35: 35 = 5 * 7

GCF: The common factor is 555, so GCF = 5.
LCM: The factors are 333, 555, and 777, so LCM = 3 * 5 * 7 = 105.

7. 24 and 40

• Prime Factorization of 24: 24 = 2³ * 3
• Prime Factorization of 40: 40 = 2³ * 5

GCF: The common factor is 232³23, so GCF = 2³ = 8.
LCM: The factors are 232³23, 333, and 555, so LCM = 2³ * 3 * 5 = 120.

8. 36 and 60

• Prime Factorization of 36: 36 = 2² * 3²
• Prime Factorization of 60: 60 = 2² * 3 * 5

GCF: The common factors are 222²22 and 333, so GCF = 2² * 3 = 12.
LCM: The factors are 222²22, 323²32, and 555, so LCM = 2² * 3² * 5 = 180.

9. 8 and 12

• Prime Factorization of 8: 8 = 2³
• Prime Factorization of 12: 12 = 2² * 3

GCF: The common factor is 222²22, so GCF = 2² = 4.
LCM: The factors are 232³23 and 333, so LCM = 2³ * 3 = 24.

10. 27 and 36

• Prime Factorization of 27: 27 = 3³
• Prime Factorization of 36: 36 = 2² * 3²

GCF: The common factor is 323²32, so GCF = 3² = 9.
LCM: The factors are 222²22 and 333³33, so LCM = 2² * 3³ = 108.

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Summary of Results:

1. 12 and 24:
   GCF = 12, LCM = 24
2. 16 and 24:
   GCF = 8, LCM = 48
3. 12 and 16:
   GCF = 4, LCM = 48
4. 9 and 12:
   GCF = 3, LCM = 36
5. 20 and 25:
   GCF = 5, LCM = 100
6. 15 and 35:
   GCF = 5, LCM = 105
7. 24 and 40:
   GCF = 8, LCM = 120
8. 36 and 60:
   GCF = 12, LCM = 180
9. 8 and 12:
   GCF = 4, LCM = 24
10. 27 and 36:
    GCF = 9, LCM = 108

Explanation:

• GCF: The greatest common factor is found by identifying the highest common divisors from the prime factorizations.
• LCM: The least common multiple is the smallest number that both numbers divide into, achieved by multiplying all prime factors at their highest powers across both numbers.