find the greatest common factor of each pair or group of numbers.
44. 20 & 15
45. 12 & 18
46. 24 & 30
47. 22 & 28
48. 20 & 40
49. 18 & 27
50. 6, 8, & 12
51. 12, 18, & 24
find the least common multiple of each pair or group of numbers
52. 8 & 10
53. 9 & 6
54. 8 & 12
55. 7 & 8
56. 9 & 12
57. 10 & 15
58. 6, 9, & 12
59. 4, 6, & 10

Question

Accepted Answer

### Problem 44: Find GCF of 20 and 15
# Explanation:
## Step1: Factorize 20 and 15
$20 = 2	imes2	imes5$, $15 = 3	imes5$
## Step2: Identify common factors
Common factor is 5.
# Answer: 5

### Problem 45: Find GCF of 12 and 18
# Explanation:
## Step1: Factorize 12 and 18
$12 = 2	imes2	imes3$, $18 = 2	imes3	imes3$
## Step2: Identify common factors
Common factors: 2, 3; product is $2	imes3 = 6$.
# Answer: 6

### Problem 46: Find GCF of 24 and 30
# Explanation:
## Step1: Factorize 24 and 30
$24 = 2	imes2	imes2	imes3$, $30 = 2	imes3	imes5$
## Step2: Identify common factors
Common factors: 2, 3; product is $2	imes3 = 6$.
# Answer: 6

### Problem 47: Find GCF of 22 and 28
# Explanation:
## Step1: Factorize 22 and 28
$22 = 2	imes11$, $28 = 2	imes2	imes7$
## Step2: Identify common factors
Common factor is 2.
# Answer: 2

### Problem 48: Find GCF of 20 and 40
# Explanation:
## Step1: Factorize 20 and 40
$20 = 2	imes2	imes5$, $40 = 2	imes2	imes2	imes5$
## Step2: Identify common factors
Common factors: $2	imes2	imes5 = 20$.
# Answer: 20

### Problem 49: Find GCF of 18 and 27
# Explanation:
## Step1: Factorize 18 and 27
$18 = 2	imes3	imes3$, $27 = 3	imes3	imes3$
## Step2: Identify common factors
Common factors: $3	imes3 = 9$.
# Answer: 9

### Problem 50: Find GCF of 6, 8, and 12
# Explanation:
## Step1: Factorize each number
$6 = 2	imes3$, $8 = 2	imes2	imes2$, $12 = 2	imes2	imes3$
## Step2: Identify common factors
Common factor is 2.
# Answer: 2

### Problem 51: Find GCF of 12, 18, and 24
# Explanation:
## Step1: Factorize each number
$12 = 2	imes2	imes3$, $18 = 2	imes3	imes3$, $24 = 2	imes2	imes2	imes3$
## Step2: Identify common factors
Common factors: 2, 3; product is $2	imes3 = 6$.
# Answer: 6

### Problem 52: Find LCM of 8 and 10
# Explanation:
## Step1: Factorize 8 and 10
$8 = 2	imes2	imes2$, $10 = 2	imes5$
## Step2: Calculate LCM (product of highest powers)
$LCM = 2^3	imes5 = 40$.
# Answer: 40

### Problem 53: Find LCM of 9 and 6
# Explanation:
## Step1: Factorize 9 and 6
$9 = 3	imes3$, $6 = 2	imes3$
## Step2: Calculate LCM (product of highest powers)
$LCM = 2	imes3^2 = 18$.
# Answer: 18

### Problem 54: Find LCM of 8 and 12
# Explanation:
## Step1: Factorize 8 and 12
$8 = 2	imes2	imes2$, $12 = 2	imes2	imes3$
## Step2: Calculate LCM (product of highest powers)
$LCM = 2^3	imes3 = 24$.
# Answer: 24

### Problem 55: Find LCM of 7 and 8
# Explanation:
## Step1: 7 and 8 are coprime (no common factors)
## Step2: LCM is product of 7 and 8
$LCM = 7	imes8 = 56$.
# Answer: 56

### Problem 56: Find LCM of 9 and 12
# Explanation:
## Step1: Factorize 9 and 12
$9 = 3	imes3$, $12 = 2	imes2	imes3$
## Step2: Calculate LCM (product of highest powers)
$LCM = 2^2	imes3^2 = 36$.
# Answer: 36

### Problem 57: Find LCM of 10 and 15
# Explanation:
## Step1: Factorize 10 and 15
$10 = 2	imes5$, $15 = 3	imes5$
## Step2: Calculate LCM (product of highest powers)
$LCM = 2	imes3	imes5 = 30$.
# Answer: 30

### Problem 58: Find LCM of 6, 9, and 12
# Explanation:
## Step1: Factorize each number
$6 = 2	imes3$, $9 = 3	imes3$, $12 = 2	imes2	imes3$
## Step2: Calculate LCM (product of highest powers)
$LCM = 2^2	imes3^2 = 36$.
# Answer: 36

### Problem 59: Find LCM of 4, 6, and 10
# Explanation:
## Step1: Factorize each number
$4 = 2	imes2$, $6 = 2	imes3$, $10 = 2	imes5$
## Step2: Calculate LCM (product of highest powers)
$LCM = 2^2	imes3	imes5 = 60$.
# Answer: 60

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 44: Find GCF of 20 and 15

Step1: Factorize 20 and 15

Step2: Identify common factors

Step1: Factorize 12 and 18

Step2: Identify common factors

Step1: Factorize 24 and 30

Step2: Identify common factors

Answer:

Problem 45: Find GCF of 12 and 18