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
Q.=Why does level of sea remain roughly same?
And:Because the water come back to sea by water cycle. Thatswhy the level of sea remains same.
To find the least number of boys the school can have, we need to find the least common multiple (LCM) of the given numbers: 12, 15, and 18.
Step 1: List the prime factors of each number:
12 = 2^2 x 3
15 = 3 x 5
18 = 2 x 3^2
Step 2: Identify the highest power of each prime factor that appears in any of the numbers:
The highest power of 2 is 2^2.
The highest power of 3 is 3^2.
The highest power of 5 is 5.
Step 3: Calculate the LCM by taking the product of the highest powers of prime factors:
LCM = 2^2 x 3^2 x 5 = 4 x 9 x 5 = 180
Therefore, the least number of boys the school can have is 180.