To find the least common multiple (LCM) of 10 and 15, follow these steps:
1. Start by listing the prime factors of each number:
- The prime factors of 10 are [tex]\(2\)[/tex] and [tex]\(5\)[/tex] (since [tex]\(10 = 2 \times 5\)[/tex]).
- The prime factors of 15 are [tex]\(3\)[/tex] and [tex]\(5\)[/tex] (since [tex]\(15 = 3 \times 5\)[/tex]).
2. Identify the highest power of each prime that appears in the factorization of both numbers:
- For the prime number [tex]\(2\)[/tex], the highest power is [tex]\(2^1\)[/tex] (which appears in the factorization of 10).
- For the prime number [tex]\(3\)[/tex], the highest power is [tex]\(3^1\)[/tex] (which appears in the factorization of 15).
- For the prime number [tex]\(5\)[/tex], the highest power is [tex]\(5^1\)[/tex] (which appears in the factorization of both numbers).
3. Multiply these highest powers together to find the LCM:
[tex]\[
\text{LCM} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5
\][/tex]
Performing the multiplication, we get:
[tex]\[
2 \times 3 = 6
\][/tex]
[tex]\[
6 \times 5 = 30
\][/tex]
Therefore, the least common multiple of 10 and 15 is 30.
