What is the smallest number of soldiers in a regiment that will allow the soldiers to be lined up in rows of exactly 8,12, or 18 and form a square each time?
Answers
Step-by-step explanation:
Given What is the smallest number of soldiers in a regiment that will allow the soldiers to be lined up in rows of exactly 8,12, or 18 and form a square each time?
- So smallest number will be least common multiple (LCM) of 8,12,18
- So factors are 2 x 2 x 2 x 3 x 3
- Since the soldiers are in the form of square, so LCM needs to be perfect square. Now we need to multiply it by 3 in order to make it a perfect square.
- So it will be 2 x 2 x 2 x 2 x 3 x 3 = 144
- So required number of soldiers will be 144
Reference link will be
https://brainly.in/question/8630983
Answer:
The number that can be lined up in 8s,12s or 18s is the LCM of these numbers.
Step-by-step explanation:
the LCM of 8,12 and 18 = 2×2×3×2×3 = 72
For the regiment to form a square, the number must be a perfect square.
But 72 is not a perfect square. We must find the least multiplier that will make 72 a perfect square.
72 = 2×2×2×3×3
Notice that out of the prime factors of 72 one 2 doesn't occur in a pair. Multiply 72 by 2 and the number 144 is a perfect square.
Thus, the least required number of soldiers in the regiment is 72×4 = 144