the boys of a school can be arranged in 12, 15, 18 equal rows and also into a solid square. what is the least number of boys that the school can have? (hint: find the lcm) anwer is 900 explain

the number has to be evenly divisible by 12,15,18.

12 = 2^2 * 3
15 = 3 * 5
18 = 2 * 3^2
LCM is thus 2^2 * 3^2 * 5 = 180

But, we want the number 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 = 900

i can't understand this method. how we can create 5?

Hello

Dear a the quedtion solved .when we ake LCM 2 comes two time and 3 also omes two time and these two digits have there perfect square so we make the perfect square of 5 and we have to b multiply with 5 again so it become perfect multiply and the answer become 900 .
2^2*3^3*5=180*5=900

Great job ....you are first...

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? (Hint:Find the LCM)

Questions 7 ex4b

To find the least number of boys that the school can have, we need to find the least common multiple (LCM) of the given numbers: 12, 15, and 18.

First, let's list the multiples of each number:
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
- Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
- Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, ...

The LCM is the smallest number that is divisible by all three given numbers. To find it, we need to look for the smallest common value in the lists of multiples.

From the lists above, we can see that the smallest common multiple of 12, 15, and 18 is 60. However, this number does not satisfy the requirement of being able to arrange the boys in a solid square.

Let's continue listing the multiples until we find a number that can be arranged into a solid square:
- Multiples of 12: ... 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, ...
- Multiples of 15: ... 135, 150, 165, 180, 195, 210, 225, 240, ...
- Multiples of 18: ... 162, 180, ...

Here, we see that 180 is the smallest common multiple that can be arranged into a solid square because it appears in all three lists.

To determine the number of boys, we can calculate the square of 180: 180 x 180 = 32,400.

However, this is the total number of students in the school. To find the number of boys, we need to divide it by the total number of rows. Since there are 12, 15, and 18 equal rows, we divide 32,400 by the LCM of the given numbers:

32,400 ÷ 180 = 180

Therefore, the least number of boys that the school can have is 180.

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