Question : What is the least number of students in a class such that they can make rows of 10,15 and 20 and also the total number of students is a perfect square?
Option 1: 6400
Option 2: 1600
Option 3: 900
Option 4: 1800
Correct Answer: 900
Solution :
The prime factorization of the numbers is as follows:
⇒ 10 = 2 × 5
⇒ 15 = 3 × 5
⇒ 20 = 2
2
× 5
Least Common Multiple (LCM) of 10, 15, and 20 = 2
2
× 3 × 5 = 60
So, the least number of students in a class such that they can make rows of 10, 15, and 20 is 60,
However, according to the question, the number of students must be a perfect square.
So, we need to multiply the LCM by 3 and 5 to make it a perfect square.
Therefore, the total number of students required = 3 × 5 × 60 = 900
Hence, the correct answer is 900.
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