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The HCF of 3 different no is 17, Which of the following cannot be their LCM ?
- a)540
- b)289
- c)340
- d)425
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The HCF of 3 different no is 17, Which of the following cannot be thei...
To check whether the given number is it's LCM or not just divide the LCM by HCF .
1) 540 ÷ 17 = 31.76
2) 289 ÷ 17 = 17
3) 340 ÷ 17 = 20
4) 425 ÷ 17 = 25 .
540 is not divisible by 17.
Hence : 540 is not the LCM .
1) 540 ÷ 17 = 31.76
2) 289 ÷ 17 = 17
3) 340 ÷ 17 = 20
4) 425 ÷ 17 = 25 .
540 is not divisible by 17.
Hence : 540 is not the LCM .
Most Upvoted Answer
The HCF of 3 different no is 17, Which of the following cannot be thei...
Introduction:
In this question, we are given that the highest common factor (HCF) of three different numbers is 17. We need to determine which of the given options cannot be their least common multiple (LCM).
Explanation:
To solve this problem, we need to understand the relationship between the HCF and LCM of numbers.
HCF and LCM Relationship:
- The HCF of two numbers is the largest number that can divide both of them.
- The LCM of two numbers is the smallest number that is divisible by both of them.
Key Point:
The HCF and LCM of two numbers have the following relationship:
- HCF * LCM = Product of the two numbers.
Approach:
1. Let's assume the three numbers are a, b, and c.
2. Given that the HCF of these three numbers is 17.
3. Let's assume their LCM is x, which we need to find.
4. According to the key point mentioned above, we have the following equation:
17 * x = a * b * c
Analysis of Options:
a) 540:
- If 540 is the LCM, then a * b * c = 17 * 540
- Since 17 is a prime number, it cannot be a factor of 540.
- Therefore, option A (540) cannot be the LCM.
b) 289:
- If 289 is the LCM, then a * b * c = 17 * 289
- Since 17 is a factor of 289 (17 * 17 = 289), it is possible for 289 to be the LCM.
- Therefore, option B (289) can be the LCM.
c) 340:
- If 340 is the LCM, then a * b * c = 17 * 340
- Since 17 is a factor of 340 (17 * 20 = 340), it is possible for 340 to be the LCM.
- Therefore, option C (340) can be the LCM.
d) 425:
- If 425 is the LCM, then a * b * c = 17 * 425
- Since 17 is a factor of 425 (17 * 25 = 425), it is possible for 425 to be the LCM.
- Therefore, option D (425) can be the LCM.
Conclusion:
From our analysis, we can see that option A (540) cannot be the LCM of the three numbers with an HCF of 17. Therefore, the correct answer is option A.
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The HCF of 3 different no is 17, Which of the following cannot be thei...
HCF&LCM of numbers are always the factors of each other
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The HCF of 3 different no is 17, Which of the following cannot be their LCM ?a)540b)289c)340d)425e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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