What is the lowest common multiple of 16 and 28?
Understand the Problem
The question is asking for the lowest common multiple (LCM) of the numbers 16 and 28. To find the LCM, we need to identify the smallest multiple that both numbers share.
Answer
The lowest common multiple of 16 and 28 is $112$.
Answer for screen readers
The lowest common multiple (LCM) of 16 and 28 is 112.
Steps to Solve
- Find the Prime Factorization of Each Number
Start by breaking down each number into its prime factors.
For 16: $$ 16 = 2^4 $$
For 28: $$ 28 = 2^2 \times 7^1 $$
- Identify the Highest Powers of Each Prime Factor
Next, we need to determine the highest power of each prime factor that appears in the factorizations.
- For the prime factor $2$, the highest power is $2^4$ (from 16).
- For the prime factor $7$, the highest power is $7^1$ (from 28).
- Calculate the Least Common Multiple (LCM)
Now, multiply the highest powers of all prime factors together to find the LCM.
$$ \text{LCM} = 2^4 \times 7^1 $$
- Perform the Multiplication
Now, calculate the result of the multiplication.
$$ \text{LCM} = 16 \times 7 = 112 $$
The lowest common multiple (LCM) of 16 and 28 is 112.
More Information
The least common multiple is useful for adding fractions with different denominators, finding common times for events, and more in various mathematical applications. The LCM helps in comparing multiples of different numbers.
Tips
- Forgetting to include all prime factors when calculating the LCM.
- Not using the highest power of each prime factor, which can lead to an incorrect LCM.
