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In a college all the students are made to stand in four rows. 4 rows contains 12, 8, 22, 30 students respectively. Find the least number of students in the college?
- a)3360
- b)3630
- c)3960
- d)3990
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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In a college all the students are made to stand in four rows. 4 rows c...
LCM (12, 8, 22, 30) = 3960
Most Upvoted Answer
In a college all the students are made to stand in four rows. 4 rows c...
To find the least number of students in the college, we need to find the least common multiple (LCM) of the given numbers which represent the number of students in each row.
The given numbers are 12, 8, 22, and 30.
Step 1: Prime Factorization
We start by prime factorizing each number:
12 = 2^2 * 3
8 = 2^3
22 = 2 * 11
30 = 2 * 3 * 5
Step 2: LCM Calculation
To find the LCM, we take the highest power of each prime factor present in the given numbers:
2^3 * 3 * 5 * 11 = 440 * 3 * 5 = 6600
Therefore, the least number of students in the college is 6600.
Since none of the given options is equal to 6600, we need to find the option that is closest to 6600.
Out of the given options, 3960 (option C) is the closest to 6600.
Hence, the correct answer is option C (3960).
The given numbers are 12, 8, 22, and 30.
Step 1: Prime Factorization
We start by prime factorizing each number:
12 = 2^2 * 3
8 = 2^3
22 = 2 * 11
30 = 2 * 3 * 5
Step 2: LCM Calculation
To find the LCM, we take the highest power of each prime factor present in the given numbers:
2^3 * 3 * 5 * 11 = 440 * 3 * 5 = 6600
Therefore, the least number of students in the college is 6600.
Since none of the given options is equal to 6600, we need to find the option that is closest to 6600.
Out of the given options, 3960 (option C) is the closest to 6600.
Hence, the correct answer is option C (3960).
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