What is the greatest common multiple of 15, 75 and 90?Responses9009001515450450
Question
What is the greatest common multiple of 15, 75 and 90?
Responses:
- 900
- 900
- 15
- 4545
- 450
Solution
To find the greatest common multiple (GCM) of the numbers 15, 75, and 90, we can follow these steps:
1. ### Break Down the Problem
We need to find the GCM of three numbers. The GCM is the smallest multiple that is common to all three numbers.
2. ### Relevant Concepts
The GCM can often be found using the prime factorization of each number or using the least common multiple (LCM) method, expressed as follows: However, for the explanation here, we'll focus on finding the direct multiples.
3. ### Analysis and Detail
Let's find the multiples of each number up to a reasonable limit:
-
Multiples of 15:
-
Multiples of 75:
-
Multiples of 90:
Now, we can see:
- The common multiples from above are , , etc.
4. ### Verify and Summarize
The smallest common multiple among the discovered common multiples is and the next one is . Therefore, the greatest common multiple of the numbers is:
Final Answer
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