Answer :
Sure! Let's find the Least Common Multiple (LCM) for each given set of numbers step-by-step.
### Set 1: Numbers 30 and 15
1. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
2. Factors of 15: 1, 3, 5, 15
The common factors between 30 and 15 are 1, 3, 5, and 15. The highest of these is 15.
3. Multiples of 30: 30, 60, 90, 120, 150, ...
4. Multiples of 15: 15, 30, 45, 60, 75, ...
The least multiple common to both lists is 30.
So, the LCM of 30 and 15 is 30.
### Set 2: Numbers 20 and 4
1. Factors of 20: 1, 2, 4, 5, 10, 20
2. Factors of 4: 1, 2, 4
The common factors are 1, 2, and 4, with 4 being the greatest.
3. Multiples of 20: 20, 40, 60, 80, 100, ...
4. Multiples of 4: 4, 8, 12, 16, 20, ...
The first common multiple is 20.
So, the LCM of 20 and 4 is 20.
### Set 3: Numbers 5, 12, and 10
To find the LCM of more than two numbers, you can find the LCM of the first two and then find the LCM of that result with the third number.
1. LCM of 5 and 12:
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
- Multiples of 12: 12, 24, 36, 48, 60, ...
The least common multiple is 60.
2. LCM of 60 (from 5 and 12) and 10:
- Multiples of 60: 60, 120, 180, ...
- Multiples of 10: 10, 20, 30, 40, 50, 60, ...
The least common multiple is 60.
So, the LCM of 5, 12, and 10 is 60.
### Set 4: Numbers 3 and 8
1. Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
2. Multiples of 8: 8, 16, 24, ...
The first common multiple is 24.
So, the LCM of 3 and 8 is 24.
### Set 5: Numbers 40, 3, and 24
1. LCM of 40 and 3:
- Multiples of 40: 40, 80, 120, ...
- Multiples of 3: 3, 6, 9, 12, 15, ..., 120, ...
The least common multiple is 120.
2. LCM of 120 (from 40 and 3) and 24:
- Multiples of 120: 120, 240, ...
- Multiples of 24: 24, 48, 72, 96, 120, ...
The least common multiple is 120.
So, the LCM of 40, 3, and 24 is 120.
To summarize:
- LCM of 30 and 15 is 30.
- LCM of 20 and 4 is 20.
- LCM of 5, 12, and 10 is 60.
- LCM of 3 and 8 is 24.
- LCM of 40, 3, and 24 is 120.
### Set 1: Numbers 30 and 15
1. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
2. Factors of 15: 1, 3, 5, 15
The common factors between 30 and 15 are 1, 3, 5, and 15. The highest of these is 15.
3. Multiples of 30: 30, 60, 90, 120, 150, ...
4. Multiples of 15: 15, 30, 45, 60, 75, ...
The least multiple common to both lists is 30.
So, the LCM of 30 and 15 is 30.
### Set 2: Numbers 20 and 4
1. Factors of 20: 1, 2, 4, 5, 10, 20
2. Factors of 4: 1, 2, 4
The common factors are 1, 2, and 4, with 4 being the greatest.
3. Multiples of 20: 20, 40, 60, 80, 100, ...
4. Multiples of 4: 4, 8, 12, 16, 20, ...
The first common multiple is 20.
So, the LCM of 20 and 4 is 20.
### Set 3: Numbers 5, 12, and 10
To find the LCM of more than two numbers, you can find the LCM of the first two and then find the LCM of that result with the third number.
1. LCM of 5 and 12:
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
- Multiples of 12: 12, 24, 36, 48, 60, ...
The least common multiple is 60.
2. LCM of 60 (from 5 and 12) and 10:
- Multiples of 60: 60, 120, 180, ...
- Multiples of 10: 10, 20, 30, 40, 50, 60, ...
The least common multiple is 60.
So, the LCM of 5, 12, and 10 is 60.
### Set 4: Numbers 3 and 8
1. Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
2. Multiples of 8: 8, 16, 24, ...
The first common multiple is 24.
So, the LCM of 3 and 8 is 24.
### Set 5: Numbers 40, 3, and 24
1. LCM of 40 and 3:
- Multiples of 40: 40, 80, 120, ...
- Multiples of 3: 3, 6, 9, 12, 15, ..., 120, ...
The least common multiple is 120.
2. LCM of 120 (from 40 and 3) and 24:
- Multiples of 120: 120, 240, ...
- Multiples of 24: 24, 48, 72, 96, 120, ...
The least common multiple is 120.
So, the LCM of 40, 3, and 24 is 120.
To summarize:
- LCM of 30 and 15 is 30.
- LCM of 20 and 4 is 20.
- LCM of 5, 12, and 10 is 60.
- LCM of 3 and 8 is 24.
- LCM of 40, 3, and 24 is 120.
