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

The hint really gives you the answer.

12 = 3*2*2
15 = 3*5
18=3*3*2
so least common multiple is 3*3*5*2*2 = 180

12 rows of 15
15 rows of 12
10 rows of 18

900

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

The LCM is the smallest number that is divisible by all the given numbers. We can find the LCM using the prime factorization method or the division method.

Prime factorization method:
1. Start by finding the prime factors of each number:
- 12 = 2 * 2 * 3
- 15 = 3 * 5
- 18 = 2 * 3 * 3
2. Write down the highest power of each prime factor that appears in any of the numbers:
- The highest power of 2 is 2^2 = 4.
- The highest power of 3 is 3^2 = 9.
- The highest power of 5 is 5^1 = 5.
3. Multiply the highest powers of each prime factor:
- LCM = 2^2 * 3^2 * 5^1 = 4 * 9 * 5 = 180.

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