Find the Greatest Common Factors and Least Common Multiple of the following numbers: 1. 12, 24, 36 2.. 10, 25, 50 3. 38, 86, 120 4. 9, 36, 72 5. 66, 142, 168
The Correct Answer and Explanation is:
To find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of the given numbers, we can follow these steps:
1. GCF and LCM of 12, 24, 36
Step 1: Prime Factorization
- 12 = 2² × 3
- 24 = 2³ × 3
- 36 = 2² × 3²
GCF: The GCF is obtained by taking the lowest powers of all the prime factors that appear in all factorizations.
GCF = 2² × 3 = 12.
LCM: The LCM is obtained by taking the highest powers of all prime factors.
LCM = 2³ × 3² = 72.
2. GCF and LCM of 10, 25, 50
Step 1: Prime Factorization
- 10 = 2 × 5
- 25 = 5²
- 50 = 2 × 5²
GCF: The GCF is the product of the lowest powers of common prime factors.
GCF = 5.
LCM: The LCM is the product of the highest powers of all prime factors.
LCM = 2 × 5² = 50.
3. GCF and LCM of 38, 86, 120
Step 1: Prime Factorization
- 38 = 2 × 19
- 86 = 2 × 43
- 120 = 2³ × 3 × 5
GCF: The GCF is the product of the lowest powers of common prime factors.
GCF = 2.
LCM: The LCM is the product of the highest powers of all prime factors.
LCM = 2³ × 3 × 5 × 19 × 43 = 2,5920.
4. GCF and LCM of 9, 36, 72
Step 1: Prime Factorization
- 9 = 3²
- 36 = 2² × 3²
- 72 = 2³ × 3²
GCF: The GCF is the product of the lowest powers of common prime factors.
GCF = 3² = 9.
LCM: The LCM is the product of the highest powers of all prime factors.
LCM = 2³ × 3² = 72.
5. GCF and LCM of 66, 142, 168
Step 1: Prime Factorization
- 66 = 2 × 3 × 11
- 142 = 2 × 71
- 168 = 2³ × 3 × 7
GCF: The GCF is the product of the lowest powers of common prime factors.
GCF = 2.
LCM: The LCM is the product of the highest powers of all prime factors.
LCM = 2³ × 3 × 7 × 11 × 71 = 1,1292.
