# 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.

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 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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