Common multiple of numbers 7 and 17 within 5 multiples (1) 14, 42 (2) 14, 30 (3) 14, 28
The Correct Answer and Explanation is:
To determine the common multiples of the numbers 7 and 17 within the first 5 multiples, we need to first list the first few multiples of each number.
Multiples of 7:
The multiples of 7 are 7, 14, 21, 28, 35, and so on.
Multiples of 17:
The multiples of 17 are 17, 34, 51, 68, 85, and so on.
Now, let’s identify the common multiples:
- The first common multiple of 7 and 17 is 119 (since 119 = 7 × 17).
Within the first 5 multiples:
- The multiples of 7 are 7, 14, 21, 28, and 35.
- The multiples of 17 are 17, 34, 51, 68, and 85.
We can see that there are no common multiples within the first 5 multiples of 7 and 17. The smallest common multiple (LCM) is 119, but it appears after the first 5 multiples.
Answer Breakdown:
- Option 1: 14, 42 – This includes multiples of 7, but not 17.
- Option 2: 14, 30 – Neither of these numbers is a multiple of 17.
- Option 3: 14, 28 – These are multiples of 7, but not 17.
Therefore, none of the options are correct based on the question’s request to find the common multiples of 7 and 17 within their first 5 multiples.
Conclusion:
The common multiple of 7 and 17 in the first few multiples is 119, but it doesn’t show up within the first 5 multiples of either number. Thus, there are no correct answers among the options provided.
