maths
posted by aliya on .
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?

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 
Find the LCM of 12,15 and 18. Then multiply the LCM the minimum number to make it perfect square, 180 x 5 = 900
find the square root of 900, which is 30 
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And:Because the water come back to sea by water cycle. Thatswhy the level of sea remains same.