What is the LCM of 4 and 18?
Understand the Problem
The question is asking us to find the least common multiple (LCM) of the numbers 4 and 18. To solve this, we will identify the multiples of both numbers and determine the smallest multiple that is common to both.
Answer
The least common multiple of 4 and 18 is \( 36 \).
Answer for screen readers
The least common multiple of 4 and 18 is ( LCM(4, 18) = 36 ).
Steps to Solve
- List the multiples of each number
First, let's find the multiples of 4. The first few multiples are: $$ 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, \ldots $$
Next, let's find the multiples of 18. The first few multiples are: $$ 18, 36, 54, 72, 90, \ldots $$
- Identify common multiples
Now, we'll look for the common multiples between the two lists. From the multiples we found:
- The multiples of 4 are: $$ 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, \ldots $$
- The multiples of 18 are: $$ 18, 36, 54, 72, 90, \ldots $$
The common multiples are: $$ 36, 72, \ldots $$
- Find the least common multiple (LCM)
The least common multiple is the smallest number that appears in both lists of multiples. From our lists, the smallest common multiple is: $$ LCM(4, 18) = 36 $$
The least common multiple of 4 and 18 is ( LCM(4, 18) = 36 ).
More Information
The least common multiple (LCM) is often used in adding or comparing fractions, as it allows for finding a common denominator. In this case, 36 is the first number that both 4 and 18 can divide into evenly, making it useful for various mathematical applications.
Tips
- Forgetting to list enough multiples: Make sure to list enough multiples to identify commonalities.
- Assuming larger numbers are always multiples: Just because a number is larger does not guarantee it is a multiple. Always check divisibility.
