lcm of 28 and 14
Understand the Problem
The question is asking to find the least common multiple (LCM) of the numbers 28 and 14. The LCM is the smallest number that is a multiple of both of the given numbers.
Answer
The least common multiple of 28 and 14 is $28$.
Answer for screen readers
The least common multiple (LCM) of 28 and 14 is $28$.
Steps to Solve
- Determine the prime factorization of each number
To find the LCM, we first need to factor both numbers into their prime factors.
For 28:
- $28 = 2^2 \times 7^1$
For 14:
- $14 = 2^1 \times 7^1$
- Identify the highest power of each prime number
Next, we take the highest power of each prime number from the factorizations:
- For the prime number 2: The highest power is $2^2$
- For the prime number 7: The highest power is $7^1$
- Calculate the LCM using the prime factors
Now, we multiply the highest powers of the prime factors:
$$ \text{LCM} = 2^2 \times 7^1 $$
- Perform the multiplication
Calculate the result:
$$ \text{LCM} = 4 \times 7 = 28 $$
The least common multiple (LCM) of 28 and 14 is $28$.
More Information
The LCM is useful in solving problems that involve adding, subtracting, or finding equivalent fractions. In this case, since 28 is itself a multiple of 14, the answer is the larger of the two numbers.
Tips
Common mistakes include:
- Forgetting to consider all prime factors.
- Not taking the highest power of common prime factors. To avoid these, always double-check the prime factorization and ensure you're using the highest powers.
