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

  1. Find the prime factorizations

Identify the prime factors of each number.

For 6: $$6 = 2 \times 3$$

For 10: $$10 = 2 \times 5$$

  1. 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 $5^1$.

  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.

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