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

  1. Understand prime factorization of the numbers

Prime factorize each number:

  • $5$ is a prime number itself, so: $5 = 5^1$
  • $6 = 2^1 imes 3^1$
  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 $5$: $5^1$
  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.

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