What is the least common multiple of 20 and 40?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 20 and 40. To find the LCM, we can identify the multiples of each number and determine the smallest multiple they share.
Answer
The least common multiple (LCM) of 20 and 40 is $40$.
Answer for screen readers
The least common multiple (LCM) of 20 and 40 is $40$.
Steps to Solve
- Identify the multiples of each number
First, let's list out some multiples of 20 and 40.
For 20:
- $20 \times 1 = 20$
- $20 \times 2 = 40$
- $20 \times 3 = 60$
- $20 \times 4 = 80$
- $20 \times 5 = 100$
For 40:
- $40 \times 1 = 40$
- $40 \times 2 = 80$
- $40 \times 3 = 120$
- $40 \times 4 = 160$
- Find the common multiples
Now, let's look for common multiples in both lists. From the lists we wrote above, we can see that:
- Multiples of 20: 20, 40, 60, 80, 100
- Multiples of 40: 40, 80, 120, 160
The common multiples are 40 and 80.
- Determine the least common multiple (LCM)
Among the common multiples, the least one is 40. Therefore, the least common multiple (LCM) of 20 and 40 is 40.
The least common multiple (LCM) of 20 and 40 is $40$.
More Information
The least common multiple is useful in various applications such as adding fractions with different denominators or finding repeating cycles in problem solving. In this case, since 40 is already a multiple of 20, it is the smallest common multiple.
Tips
- Ignoring the multiples altogether and trying to find the LCM using prime factorization without checking for basic multiples first.
- Miscounting or skipping numbers while listing out multiples can lead to an incorrect LCM.
