What is the LCM of 5 and 6?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 5 and 6. To solve this, we need to identify the smallest multiple that is common to both numbers.
Answer
30
Answer for screen readers
The final answer is 30
Steps to Solve
- Understand prime factorization of the numbers
Prime factorize each number:
- $5$ is a prime number itself, so: $5 = 5^1$
- $6 = 2^1 imes 3^1$
- Identify the highest power of each prime number
List out the prime factors with the highest powers that appear in any of the factorizations:
- For $2$: $2^1$
- For $3$: $3^1$
- For $5$: $5^1$
- Multiply the highest powers of each prime together
The Least Common Multiple (LCM) is the product of the highest powers of all prime factors:
$$ ext{LCM} = 2^1 imes 3^1 imes 5^1 = 30$$
The final answer is 30
More Information
The LCM is useful for solving problems where you need a common multiple of numbers, such as finding schedules, adding fractions with different denominators, or solving Diophantine equations.
Tips
A common mistake is to not use the highest power of each prime factor when calculating the LCM. Always ensure to include the highest power for all distinct prime factors involved.
