Question
The least common multiple of 20 and 14 is
Answers
GPT-4o mini
To find the least common multiple (LCM) of 20 and 14, we can use the prime factorization method.
First, we find the prime factorizations of the two numbers:
- \( 20 = 2^2 \times 5^1 \)
- \( 14 = 2^1 \times 7^1 \)
Next, for the LCM, we take the highest power of each prime number that appears in the factorizations.
- For the prime \( 2 \), the highest power is \( 2^2 \) (from 20).
- For the prime \( 5 \), the highest power is \( 5^1 \) (from 20).
- For the prime \( 7 \), the highest power is \( 7^1 \) (from 14).
Now we can calculate the LCM:
\[
LCM = 2^2 \times 5^1 \times 7^1 = 4 \times 5 \times 7
\]
Calculating this step by step:
1. \( 4 \times 5 = 20 \)
2. \( 20 \times 7 = 140 \)
Thus, the least common multiple of 20 and 14 is \( \boxed{140} \).
First, we find the prime factorizations of the two numbers:
- \( 20 = 2^2 \times 5^1 \)
- \( 14 = 2^1 \times 7^1 \)
Next, for the LCM, we take the highest power of each prime number that appears in the factorizations.
- For the prime \( 2 \), the highest power is \( 2^2 \) (from 20).
- For the prime \( 5 \), the highest power is \( 5^1 \) (from 20).
- For the prime \( 7 \), the highest power is \( 7^1 \) (from 14).
Now we can calculate the LCM:
\[
LCM = 2^2 \times 5^1 \times 7^1 = 4 \times 5 \times 7
\]
Calculating this step by step:
1. \( 4 \times 5 = 20 \)
2. \( 20 \times 7 = 140 \)
Thus, the least common multiple of 20 and 14 is \( \boxed{140} \).