What is the LCM of 32 and 48?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 32 and 48. To find the LCM, we will identify the multiples of the two numbers and find the smallest one that is common to both lists.
Answer
$96$
Answer for screen readers
The least common multiple of 32 and 48 is $96$.
Steps to Solve
- List the multiples of each number
We start by listing some multiples of 32 and 48.
Multiples of 32:
$32, 64, 96, 128, 160, 192, 224, 256, 288, 320$
Multiples of 48:
$48, 96, 144, 192, 240, 288, 336, 384$
- Identify common multiples
Next, we identify the common multiples from both lists.
From our lists, the common multiples are:
$96, 192, 288$
- Find the least common multiple
Now we can pick the smallest number from the common multiples. The least common multiple (LCM) of 32 and 48 is $96$.
The least common multiple of 32 and 48 is $96$.
More Information
The least common multiple is useful in various mathematical operations, especially when adding or subtracting fractions with different denominators. Recognizing patterns in multiples can simplify this process.
Tips
- One common mistake is only finding the first common multiple and assuming it's the LCM. Ensure to list enough multiples to find the smallest one correctly.
- Another mistake is failing to check both lists of multiples completely.
