lcm 8 12
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 8 and 12. To solve this, we will find the multiples of each number and determine the smallest common multiple.
Answer
24
Answer for screen readers
The final answer is 24
Steps to Solve
- List the prime factors of each number
We start by finding the prime factors of 8 and 12.
$$ 8 = 2^3 $$ $$ 12 = 2^2 \cdot 3 $$
- Identify the highest powers of all prime factors
We need to take the highest power of each prime factor that appears in the factorizations.
The prime factors are 2 and 3:
- The highest power of 2 is $2^3$
- The highest power of 3 is $3^1$
- Calculate the LCM by multiplying these highest powers together
$$ \text{LCM}(8, 12) = 2^3 \cdot 3^1 $$ $$ \text{LCM}(8, 12) = 8 \cdot 3 $$ $$ \text{LCM}(8, 12) = 24 $$
The final answer is 24
More Information
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. LCM is useful in problems involving synchronization of repeating events, such as finding when two lights will blink together.
Tips
A common mistake is to add or average the numbers instead of finding the least common multiple through prime factorization.
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