Answer :
Sure, let's determine the Highest Common Factor (HCF) and the Least Common Multiple (LCM) for each of the given sets of numbers.
### Part a: Numbers 18, 20, and 30
1. Finding the HCF:
- For 18 and 20, factors are:
- 18: 1, 2, 3, 6, 9, 18
- 20: 1, 2, 4, 5, 10, 20
- Common factors: 1, 2
- HCF of 18 and 20 is 2.
- HCF of 2 and 30 (factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30):
- Common factors with 2 (already calculated): 1, 2
- HCF of all three: 2.
2. Finding the LCM:
- For 18 and 20:
- Multiply them: 18 20 = 360
- Divide by their HCF: 360 / 2 = 180
- LCM of 18 and 20 is 180.
- LCM of 180 and 30:
- Multiply them: 180 30 = 5400
- Divide by their HCF: 5400 / 30 = 180
- LCM of all three: 180.
Therefore, for 18, 20, and 30, the HCF is 2 and the LCM is 180.
### Part b: Numbers 9, 16, and 12
1. Finding the HCF:
- For 9 and 16, factors are:
- 9: 1, 3, 9
- 16: 1, 2, 4, 8, 16
- Common factor: 1
- HCF of 9 and 16 is 1.
- HCF of 1 and 12 (factors of 12 are: 1, 2, 3, 4, 6, 12):
- Common factor with 1: 1
- HCF of all three: 1.
2. Finding the LCM:
- For 9 and 16:
- Multiply them: 9 16 = 144
- Divide by their HCF: 144 / 1 = 144
- LCM of 9 and 16 is 144.
- LCM of 144 and 12:
- Multiply them: 144 12 = 1728
- Divide by their HCF: 1728 / 12 = 144
- LCM of all three: 144.
Therefore, for 9, 16, and 12, the HCF is 1 and the LCM is 144.
### Part c: Numbers 8, 18, and 50
1. Finding the HCF:
- For 8 and 18, factors are:
- 8: 1, 2, 4, 8
- 18: 1, 2, 3, 6, 9, 18
- Common factor: 1, 2
- HCF of 8 and 18 is 2.
- HCF of 2 and 50 (factors of 50 are: 1, 2, 5, 10, 25, 50):
- Common factor with 2: 2
- HCF of all three: 2.
2. Finding the LCM:
- For 8 and 18:
- Multiply them: 8 18 = 144
- Divide by their HCF: 144 / 2 = 72
- LCM of 8 and 18 is 72.
- LCM of 72 and 50:
- Multiply them: 72 50 = 3600
- Divide by their HCF: 3600 / 2 = 1800
- LCM of all three: 1800.
Therefore, for 8, 18, and 50, the HCF is 2 and the LCM is 1800.
In summary:
- For 18, 20, and 30, the HCF is 2 and the LCM is 180.
- For 9, 16, and 12, the HCF is 1 and the LCM is 144.
- For 8, 18, and 50, the HCF is 2 and the LCM is 1800.
### Part a: Numbers 18, 20, and 30
1. Finding the HCF:
- For 18 and 20, factors are:
- 18: 1, 2, 3, 6, 9, 18
- 20: 1, 2, 4, 5, 10, 20
- Common factors: 1, 2
- HCF of 18 and 20 is 2.
- HCF of 2 and 30 (factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30):
- Common factors with 2 (already calculated): 1, 2
- HCF of all three: 2.
2. Finding the LCM:
- For 18 and 20:
- Multiply them: 18 20 = 360
- Divide by their HCF: 360 / 2 = 180
- LCM of 18 and 20 is 180.
- LCM of 180 and 30:
- Multiply them: 180 30 = 5400
- Divide by their HCF: 5400 / 30 = 180
- LCM of all three: 180.
Therefore, for 18, 20, and 30, the HCF is 2 and the LCM is 180.
### Part b: Numbers 9, 16, and 12
1. Finding the HCF:
- For 9 and 16, factors are:
- 9: 1, 3, 9
- 16: 1, 2, 4, 8, 16
- Common factor: 1
- HCF of 9 and 16 is 1.
- HCF of 1 and 12 (factors of 12 are: 1, 2, 3, 4, 6, 12):
- Common factor with 1: 1
- HCF of all three: 1.
2. Finding the LCM:
- For 9 and 16:
- Multiply them: 9 16 = 144
- Divide by their HCF: 144 / 1 = 144
- LCM of 9 and 16 is 144.
- LCM of 144 and 12:
- Multiply them: 144 12 = 1728
- Divide by their HCF: 1728 / 12 = 144
- LCM of all three: 144.
Therefore, for 9, 16, and 12, the HCF is 1 and the LCM is 144.
### Part c: Numbers 8, 18, and 50
1. Finding the HCF:
- For 8 and 18, factors are:
- 8: 1, 2, 4, 8
- 18: 1, 2, 3, 6, 9, 18
- Common factor: 1, 2
- HCF of 8 and 18 is 2.
- HCF of 2 and 50 (factors of 50 are: 1, 2, 5, 10, 25, 50):
- Common factor with 2: 2
- HCF of all three: 2.
2. Finding the LCM:
- For 8 and 18:
- Multiply them: 8 18 = 144
- Divide by their HCF: 144 / 2 = 72
- LCM of 8 and 18 is 72.
- LCM of 72 and 50:
- Multiply them: 72 50 = 3600
- Divide by their HCF: 3600 / 2 = 1800
- LCM of all three: 1800.
Therefore, for 8, 18, and 50, the HCF is 2 and the LCM is 1800.
In summary:
- For 18, 20, and 30, the HCF is 2 and the LCM is 180.
- For 9, 16, and 12, the HCF is 1 and the LCM is 144.
- For 8, 18, and 50, the HCF is 2 and the LCM is 1800.
