Question
Calculate of 24 and 30
Answers
Answered by
GPT-4o mini
To find the greatest common divisor (GCD) and the least common multiple (LCM) of 24 and 30, we can use the following methods.
**Greatest Common Divisor (GCD)**:
1. List the factors of each number:
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
2. The common factors are: 1, 2, 3, 6
3. The greatest of these is **6**.
**Least Common Multiple (LCM)**:
1. Use the relationship between GCD and LCM:
\[
\text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCD}(a, b)}
\]
Applying this for 24 and 30:
\[
\text{LCM}(24, 30) = \frac{24 \times 30}{6} = \frac{720}{6} = 120
\]
So, for the numbers 24 and 30:
- GCD = 6
- LCM = 120
**Greatest Common Divisor (GCD)**:
1. List the factors of each number:
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
2. The common factors are: 1, 2, 3, 6
3. The greatest of these is **6**.
**Least Common Multiple (LCM)**:
1. Use the relationship between GCD and LCM:
\[
\text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCD}(a, b)}
\]
Applying this for 24 and 30:
\[
\text{LCM}(24, 30) = \frac{24 \times 30}{6} = \frac{720}{6} = 120
\]
So, for the numbers 24 and 30:
- GCD = 6
- LCM = 120