What is the least common multiple of 8 and 36?
Understand the Problem
The question is asking to find the least common multiple (LCM) of the numbers 8 and 36. To solve this, we will determine the multiples of each number and identify the smallest common multiple between them.
Answer
$72$
Answer for screen readers
The least common multiple (LCM) of 8 and 36 is $72$.
Steps to Solve
- List the multiples of each number
Start by generating the multiples of both 8 and 36.
For 8, the first few multiples are:
- $8, 16, 24, 32, 40, 48, 56, 64, 72, \ldots$
For 36, the first few multiples are:
- $36, 72, 108, 144, \ldots$
- Identify the common multiples
Now, look for common multiples in the lists generated.
The common multiples of 8 and 36 from our lists are:
- $72, 144, \ldots$
- Select the least common multiple
From the common multiples found, determine the smallest one.
The least common multiple (LCM) is:
- $72$
The least common multiple (LCM) of 8 and 36 is $72$.
More Information
The least common multiple (LCM) is a useful concept in mathematics, especially in tasks that involve finding common denominators in fractions. Knowing that $72$ is the LCM helps in simplifying fraction operations involving these numbers.
Tips
- One common mistake is only listing a few multiples and assuming they are sufficient, leading to missing the correct LCM. To avoid this, ensure to list enough multiples to accurately identify common ones.
- Another mistake can be confusing LCM with the greatest common divisor (GCD). It's important to recognize that LCM is the smallest multiple that two numbers share, while GCD is the largest divisor they share.
