Question

in a school auditorium there are three types of row arrangements possible for watching a program:rows of 30 students in each row or rows of 40 students in each row or rows of 45 students in each row what is the least number of students so that all the students can be accommodated in each of these arrangements​

Answer 1

Explanation:

To find the least number of students that can be accommodated in each of these arrangements, we need to find the least common multiple (LCM) of the numbers 30, 40, and 45.

We can find the LCM by finding the prime factorization of each number and then multiplying the highest powers of each prime factor:

30 = 2 x 3 x 5

40 = 2^3 x 5

45 = 3^2 x 5

The LCM is then the product of the highest powers of each prime factor:

LCM = 2^3 x 3^2 x 5 = 360

Therefore, the least number of students that can be accommodated in each of these arrangements is 360.

In rows of 30 students, there would be 12 rows (30 x 12 = 360).

In rows of 40 students, there would be 9 rows (40 x 9 = 360).

In rows of 45 students, there would be 8 rows (45 x 8 = 360).

So, regardless of the row arrangement chosen, a total of 360 students can be accommodated.