What is the lowest common multiple of 6 and 10?
Understand the Problem
The question is asking for the lowest common multiple (LCM) of the numbers 6 and 10, which involves finding the smallest number that is a multiple of both 6 and 10.
Answer
30
Answer for screen readers
The final answer is 30
Steps to Solve
- Find the prime factorizations
Identify the prime factors of each number.
For 6: $$6 = 2 \times 3$$
For 10: $$10 = 2 \times 5$$
- Identify the highest powers of each prime factor
The prime factors of 6 are 2 and 3. The prime factors of 10 are 2 and 5. We take the highest power of each prime factor from both factorizations.
The highest power of 2 is $2^1$. The highest power of 3 is $3^1$. The highest power of 5 is $5^1$.
- Multiply these highest powers together
Multiply the highest powers of each prime factor together to get the LCM:
$$LCM = 2^1 \times 3^1 \times 5^1$$
$$LCM = 2 \times 3 \times 5$$
$$LCM = 30$$
The final answer is 30
More Information
The LCM is useful in problems involving adding or subtracting fractions with different denominators or finding common time intervals.
Tips
A common mistake is to incorrectly identify the prime factors of a number or to not use the highest power of each prime factor when calculating the LCM.
