GCM for 16 and 24
Understand the Problem
The question is asking for the greatest common multiple (GCM) of the numbers 16 and 24, which involves finding the largest multiple that two or more numbers share.
Answer
The greatest common multiple of 16 and 24 is $96$.
Answer for screen readers
The greatest common multiple (GCM) of 16 and 24 is $96$.
Steps to Solve
- List the Multiples of Each Number
We start by listing out the first few multiples of 16 and 24.
Multiples of 16:
- $16, 32, 48, 64, 80, 96, 112, \ldots$
Multiples of 24:
- $24, 48, 72, 96, 120, \ldots$
- Identify the Common Multiples
Next, we look for common multiples in the lists we created.
From our lists:
- Common multiples are $48, 96, \ldots$
- Determine the Greatest Common Multiple
Now, we need to find the greatest common multiple from the identified common multiples.
The largest common multiple we've found is $96$. Hence, the greatest common multiple of 16 and 24 is $96$.
The greatest common multiple (GCM) of 16 and 24 is $96$.
More Information
The greatest common multiple is the largest number that is a multiple of both numbers. In this case, both 16 and 24 share multiples, and the highest one they both include is 96. Understanding GCM is particularly useful in problems involving fractions and synchronization of cycles.
Tips
- Confusing least common multiple (LCM) with greatest common multiple (GCM). GCM is about finding the maximum shared multiple, whereas LCM finds the smallest shared multiple.
- Failing to list enough multiples to find the highest common one. Always be sure to extend your list sufficiently.
