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.
Answer
24
Answer for screen readers
The LCM of 8 and 12 is 24.
Steps to Solve
- 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: $$ 12 = 2 \times 2 \times 3 = 2^2 \times 3^1 $$
- 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 $$3^1$$.
- 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.
More Information
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.