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.

Answer

30
Answer for screen readers

The final answer is 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.

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

The final answer is 30

More Information

The LCM is useful when adding, subtracting, or comparing fractions with different denominators.

Tips

A common mistake is to forget to use the highest power of each prime factor when calculating the LCM.

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