On the playground, if children are made to stand to drill either 20 to a row or 25 to a row, all rows are complete and no child is left out. What Is the lowest possible number of children in that school ?

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200

100

answer is D.

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Detailed Solution

Concept- Concept of LCM will be used here prime factorization: In number theory, prime factorisation is the method of expressing a composite number into a product of prime numbers, smaller than the original number. This process is carried out by dividing with the prime number and finding the quotient, thus writing the number as the prime x quotient.
Given conditions, students are arranged 20 per row or 25 per row,with zero students left. Assume that it takes “a” rows if the students are arranged such as 20 students per row to complete all of them. By the above statement, we can say the total number of students. Total number of the students = 20×a
Let us assume the total number of students as the variable k. Above equation in terms of the variable k can be written as - k = 20×a
Let’s assume that it takes “b” rows if the students are arranged such as 25 students per row to complete all. We can write an equation in terms of k, given in the form of , k = 25b.
So, k is the multiple of 20 and 25, we need the least value of “k” which is a multiple of both 20 and 25. So, It can be said that the required value k is nothing but the least common multiple of 20, 25. We need to prime factorise both.
This process is being carried out by dividing with prime numbers and finding quotients thus writing numbers as prime x quotients. Repeat the process for the quotient till one as the quotient is derived.
By dividing 20 by 2, we can write 20 = 2×10
By dividing 10 by 2, we can write 20 = 2×2×5
By dividing 5 by 5, we can write 20 = 2×2×5×1
We need to stop, as we have got one as the quotient.
By dividing 25 by 5, we can write 25 = 5×5
By dividing 5 by 5, we can write
25 = 5×5×1
We need to stop, as we have got one as the quotient..
By writing both of the above equations together, we get it as
20 = 2×2×5
25 = 5×5
We can combine one of the “5” as common between both and write least common multiple of 20, 25 in form of LCM(20,25) = 5×5×2×2 = 100
Therefore there must be a minimum of 100 students to and for a drill in any row between 20 & 25.
Hence, the current option is 4.

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