Question

Find the smallest perfect square which is divisible by the 9,10,11 and also find it square root

Answer 1

Answer:

first find LCM of three no's,9,10,11,i.e,990

990=2*495,

=2*5*99,

=2*5*3*33,

=2*5*3*3*11,

so the smallest perfect square which is divisible by 9,10,11 is (990)^2 and it's square root is 990.

Hope it helps u...

Answer 2

The smallest perfect square which is divisible by the 9,10,11 is 108900  

And √108900 = 330

Given:

Numbers 9, 10, 11

To find:

The smallest perfect square which is divisible by the 9,10,11 and also find it square root

Solution:

To find the smallest perfect square which is divisible by the 9,10,11

first find the LCM of 9, 10 and 11 as given below  

Write the given numbers as product of prime numbers

9 = 3 × 3

10 = 2 × 5

11 = 1 × 11  

LCM (10, 11, 9) = 2 × 3 × 3 × 5 × 11 = 990

Now write 990 as product of prime numbers

990 =  2 × 3 × 3 × 5 × 11

Now group the factors as squares

= 2 × 3² × 5 × 11

After grouping factor 2, 5 and 11 are left alone

Here, to get a perfect square number we need one 2, one 5 and one 11

⇒ 2 × 5 × 11 = 110

Now, 990 × 110 will be a square number

⇒ 990 × 110 = 108900  

The smallest perfect square which is divisible by the 9,10,11 is 108900  

As we know

108900 = 990 × 110 = 2 × 3² × 5 × 11 × 2 × 5 × 11  

⇒ √108900 =√2² × 3²× 5² × 11²

= 2 × 3 × 5 × 11 = 330

√108900 = 330

Therefore,

The smallest perfect square which is divisible by the 9,10,11 is 108900  

And √108900 = 330

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