# What is the LCM of 8 and 12?

#### Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 8 and 12. To solve it, we will identify the multiples of both numbers and find the smallest multiple they share.

24

The LCM of 8 and 12 is 24.

#### Steps to Solve

1. Find the prime factorization of each number

8 can be factorized to prime factors as follows: $$8 = 2 \times 2 \times 2 = 2^3$$ 12 can be factorized to prime factors as follows: $$12 = 2 \times 2 \times 3 = 2^2 \times 3^1$$

1. Determine the highest power of each prime number

We choose the highest power of each prime number appearing in the factorization of both numbers:

• For 2, the highest power is $$2^3$$.
• For 3, the highest power is $$3^1$$.
1. Multiply these highest powers to find the LCM

The LCM is obtained by multiplying these highest powers together: $$LCM = 2^3 \times 3^1 = 8 \times 3 = 24$$

The LCM of 8 and 12 is 24.

The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both of the numbers.

#### Tips

A common mistake is to add or multiply the prime factors incorrectly. Always ensure you pick the highest powers of each prime from the factorizations.

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