Question

The students in a School can be arranged in 12,15 and 18 equal rows and also into a solid square. What is the lowest number of students that can be in the school ​

Answer 1

Answer:

900 students

Step-by-step explanation:

The number we are looking for has to be

1. evenly divisible by 12, 15 & 18

and

2. be a perfect square

1---------------------

• Lets find prime factors of the given numbers:

• 12 = 2*2*3
• 15 = 3*5
• 18 = 2*3*3
• LCM(12,15,18) =2*2*3*3*5 = 180

We have met the first condition

2---------------------

The number, in the format 2^2*3^2*5 needs to be a perfect square

Since it already is a multiple of 2^2 and 3^2, we just need to add a factor of 5 to get 5^2.

180*5 = (2*3*5)^2= 900

Now we met the second condition and got the answer: 900

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