# What is the lowest common multiple of 10 and 15?

#### Understand the Problem

The question is asking for the lowest common multiple (LCM) of the numbers 10 and 15. The LCM is the smallest number that is a multiple of both 10 and 15, which can be determined by finding the multiples of both numbers and identifying the smallest common one.

30

#### Steps to Solve

1. Find the prime factorization of each number

Factor each number into its prime factors.

$$10 = 2 \times 5$$ $$15 = 3 \times 5$$

1. Identify the highest power of each prime number

Look at the prime factors from both factorizations and select the highest power of each prime number.

• The prime factors are 2, 3, and 5.
• Highest power of 2 = $2^1$
• Highest power of 3 = $3^1$
• Highest power of 5 = $5^1$
1. Multiply the highest powers together

Multiply these highest powers to determine the LCM.

$$LCM = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5$$

1. Calculate the result

Calculate the final result.

$$LCM = 2 \times 3 \times 5 = 30$$