Question

Find the smallest square number that is divisible by each 8,9 and 10.
How many non perfect square numbers lie between .

Answer 1

Answer:

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Step-by-step explanation

3600

The smallest square number divisible by 8,9,10=3600.

Smallest Square number is 3600.

Step-by-step explanation:

To find: Smallest Square number divisible by 8 , 9 , 10

Prime Factorization to find LCM,

8 = 2 × 2 × 2

9 = 3 × 3

10 = 2 × 5

LCM ( 8 , 9 , 10 ) = 2 × 2 × 2 × 3 × 3 × 5 = 360

Clearly 360 but it is not a perfect square number.

Now we make the pairs complete by multiplying same numbers in prime factorization of LCM.

We need one 2 and one 5 to complete the pair.

We get, Least Square number = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 3600

Therefore, Smallest Square Number is 3600.