Question

find the smallest whole square number which is completely devided by 16 18 and 45​

Answer 1

Step-by-step explanation:

16 = 2x2x2x2

18 = 2x3x3

45 = 3x3x5

LCM = 2^4x3^2x5 = 720

720x5 = 3600 is the least perfect square divisible by 16, 18 and 45.

Answer 2

Solution :-

According to the question,

We want smallest square number which is completely divisible by 16 , 18 and 45

In order to do this question,

We need to find the least common number. It means we need to do the LCM of 16 , 18 and 45

Therefore,

Prime factorization of 16 = 2 * 2 * 2 * 2

Prime factorization of 18 = 2 * 3 * 3

Prime factorization of 45 = 5 * 3 * 3

Now,

LCM of 16 , 18 and 45

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

= 2^4 * 3^2 * 5

= 720

Here, You can observed that 2 has 4 pairs, 3 has two pairs but we don't have the pair of 5 . So in order to find the pair we need to multiply 720 by 5 . So that it can be a perfect square.

Therefore,

= 720 * 5

= 3600

Therefore, The least perfect square number = 3600 $.$