The students in a school can be arranged in 12, 15 and 18 equal rows and also into a square formation. What is the lowest number of students that can be in the school?
explain plz
Answers
Answer:
You need the smallest square that is a multiple of 12, 15 and 18. Prime factorisations give you 2 x 2 x 3, 3 x 5, and 2 x 3 x 3. The number you want must have at least as many twos, at least as many threes, and at least as many fives, in its prime factorisation as any of these (so it must include at least 2 x 2, because the first does); and also, it must have an even number of each prime factor (because all squares do). You can probably finish off with that much of a hint.
Answer:
the number has to be evenly divisible by 12,15,18.
12 = 2^2 * 3
15 = 3 * 5
18 = 2 * 3^2
LCM is thus 2^2 * 3^2 * 5 = 180
But, we want the number to be a perfect square. Since it already is a multiple of 2^2 and 3^2, we just need to add a factor of 5 to get 5^2.
180*5 = 900