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 find the smallest number that is a multiple of both 16 and 12.
Answer
48
Answer for screen readers
The final answer is 48
Steps to Solve
- Prime Factorize Both Numbers
Prime factorize both numbers to determine their prime factors.
- 16 = 2^4
- 12 = 2^2 \cdot 3
- Determine the Highest Powers of Each Prime
Consider the highest powers of each prime number from the factorizations.
- For 2, the highest power is 2^4.
- For 3, the highest power is 3.
- Multiply the Highest Powers of Each Prime
Multiply the highest powers of each prime factor to find the LCM.
$$ LCM = 2^4 \cdot 3 = 16 \cdot 3 = 48 $$
The final answer is 48
More Information
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both of them. 48 is the smallest number that both 16 and 12 can divide without leaving a remainder.
Tips
A common mistake is to multiply the numbers directly without breaking them into their prime factors, which can lead to incorrect results.
