Question

What is the least number of soldiers that can be
drawn up in troops of 12, 15 18 and 20 soldiers
and also in form of a square?
(a) 900
(b) 400
(c) 1600
(d) 2500​

Answer 1

Answer :

Option (A), 900 soliders can be drawn up in the form of a square.

Step-by-step solution:

In this type of problems, we find the LCM of three numbers first and then we look for what makes the LCM a perfect square.

1st term = 12 = 2 * 2 * 3

2nd term = 15 = 3 * 5

3rd term = 18 = 2 * 3 * 3

4th term = 20 = 2 * 2 * 5

Hence, LCM (12, 15, 18, 20)

= 2 * 2 * 3 * 3 * 5 = 180

Since the LCM = 180 is not a perfect square, we make it a perfect square by multiplying 5 (which is the least value to be multiplied).

Then 180 * 5 = 900 = 30², a perfect square.

Therefore, 900 soliders can be drawn up in the form of a square.