Posted by **aliya** on Tuesday, May 15, 2012 at 3:30pm.

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

- maths -
**Steve**, Tuesday, May 15, 2012 at 5:10pm
12 = 2^2 * 3

15 = 3 * 5

18 = 2 * 3^2

LCM is 2^2 * 3^2 * 5 = 180

but, we want a perfect square, so we need an extra factor of 5, so

(2*3*5)^2 = 900

900 = 12 * 75

900 = 15 * 60

900 = 18 * 50

900 = 30^2

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