LCM of 16 and 30
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 16 and 30. To find this, we will identify the multiples of both numbers and determine the smallest multiple that they share.
Answer
$480$
Answer for screen readers
The least common multiple of 16 and 30 is $480$.
Steps to Solve
- List the multiples of both numbers
Start by listing the first few multiples of 16 and 30.
For 16:
- $16 \times 1 = 16$
- $16 \times 2 = 32$
- $16 \times 3 = 48$
- $16 \times 4 = 64$
- $16 \times 5 = 80$
- $16 \times 6 = 96$
- $16 \times 7 = 112$
- $16 \times 8 = 128$
- $16 \times 9 = 144$
- $16 \times 10 = 160$
For 30:
- $30 \times 1 = 30$
- $30 \times 2 = 60$
- $30 \times 3 = 90$
- $30 \times 4 = 120$
- $30 \times 5 = 150$
- $30 \times 6 = 180$
- $30 \times 7 = 210$
- $30 \times 8 = 240$
- Identify the common multiples
Now, identify the common multiples from the lists you've made.
From our lists:
- Common multiples include: 480, 960, etc.
- Determine the least common multiple
The smallest common multiple from the lists above is 480.
Thus, the least common multiple (LCM) of 16 and 30 is: $$ \text{LCM}(16, 30) = 480 $$
The least common multiple of 16 and 30 is $480$.
More Information
The LCM is essential in finding a common denominator for fractions, solving problems that involve syncing cycles, and more. It represents the smallest number that is a multiple of both integers.
Tips
- Focusing too much on finding all multiples rather than using the prime factorization method can lead to unnecessary work.
- Ignoring the method of using the formula $LCM(a, b) = \frac{|a \cdot b|}{GCD(a, b)}$ can simplify the calculation.
