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In a college, all the students can stand in a row, so that each row has 9, 7 and 12 students. Find the least no of students in the school ?
- a)145
- b)265
- c)186
- d)252
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a college, all the students can stand in a row, so that each row ha...
LCM of 9, 7 and 12 = 252
Most Upvoted Answer
In a college, all the students can stand in a row, so that each row ha...
Approach:
- The least number of students in the school will be the LCM of 9, 7, and 12.
- We can find the LCM by prime factorizing the numbers and taking the highest power of each prime factor.
- Once we have the LCM, we can check if it satisfies the given conditions.
Solution:
- Prime factorizing 9: 3^2
- Prime factorizing 7: 7
- Prime factorizing 12: 2^2 * 3
- Taking the highest power of each prime factor: 2^2 * 3^2 * 7 = 252
- So the least number of students in the school is 252.
- We can check if 252 satisfies the given conditions:
- 252/9 = 28 (rows of 9 students)
- 252/7 = 36 (rows of 7 students)
- 252/12 = 21 (rows of 12 students)
- So 252 satisfies the given conditions.
- Therefore, the correct answer is option D) 252.
- The least number of students in the school will be the LCM of 9, 7, and 12.
- We can find the LCM by prime factorizing the numbers and taking the highest power of each prime factor.
- Once we have the LCM, we can check if it satisfies the given conditions.
Solution:
- Prime factorizing 9: 3^2
- Prime factorizing 7: 7
- Prime factorizing 12: 2^2 * 3
- Taking the highest power of each prime factor: 2^2 * 3^2 * 7 = 252
- So the least number of students in the school is 252.
- We can check if 252 satisfies the given conditions:
- 252/9 = 28 (rows of 9 students)
- 252/7 = 36 (rows of 7 students)
- 252/12 = 21 (rows of 12 students)
- So 252 satisfies the given conditions.
- Therefore, the correct answer is option D) 252.
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In a college, all the students can stand in a row, so that each row has 9, 7 and 12 students. Find the least no of students in the school ?a)145b)265c)186d)252e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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