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
- Find the prime factorization of each number
Factor each number into its prime factors.
$$10 = 2 \times 5$$ $$15 = 3 \times 5$$
- 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 = $5^1$
- Multiply the highest powers together
Multiply these highest powers to determine the LCM.
$$LCM = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5$$
- 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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