LCM of 16 and 12
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 16 and 12. To solve this, we need to identify the multiples of each number and find the smallest multiple that is common to both.
Answer
48
Answer for screen readers
The final answer is 48
Steps to Solve
- Finding the prime factors of each number
To find the LCM, start by finding the prime factors of each number. For 16, the prime factors are: $16 = 2^4$ For 12, the prime factors are: $12 = 2^2 imes 3$
- Identify the highest powers of all prime factors
The LCM is found by taking the highest power of all prime factors present in the numbers. The prime factors are 2 and 3.
- The highest power of 2 is $2^4$.
- The highest power of 3 is $3^1$.
- Multiply the highest powers together to get the LCM
Multiply the highest powers of the prime factors to get the LCM. $$2^4 imes 3^1 = 16 imes 3 = 48$$
The final answer is 48
More Information
The least common multiple (LCM) of two or more numbers is the smallest number that is evenly divisible by all the numbers in the set. The LCM is useful in solving problems involving fractions, synchronization of cycles, and much more.
Tips
A common mistake when finding the LCM through prime factorization is not identifying the highest powers of each prime factor correctly. Always double-check your factorization to avoid errors.
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