The boys can be arranged in 12, 15 and 18 equal rows and also into a solid square what is the least number of boys that school have?

Question

(Hint: find the LCM)

Answer 1

The question states that the boys can also be arranged in a solid square, meaning that 180 cannot be the answer, as its square root is not a whole number.

 

You need a number that contains the factors 12, 15, 18, and is also a perfect square of a whole number.

 

That would be 900, which is a multiple of the three factors and is the square of 30.

 

Hope this helps.

 

Matt in NY

Answer 2

The LCM (least common multiple) is an important number/concept. It is easily found by finding the union of the sets of the prime factors of the numbers.

So, the prime factors:

   12       {2, 2, 3}
   15       {3, 5}
   18       {2, 3, 3}

Now find the smallest (least) superset that contains all three of these sets.
     It is {2, 2, 3, 3, 5}
So, the LCM = 2 * 2 * 3 * 3 * 5 = 180

 

p.s., I don't know what Square Root has to do with this.