Aptitude - Square Root and Cube Root - Discussion

Discussion :: Square Root and Cube Root - General Questions (Q.No.3)

3. 

The least perfect square, which is divisible by each of 21, 36 and 66 is:

[A]. 213444
[B]. 214344
[C]. 214434
[D]. 231444

Answer: Option A

Explanation:

L.C.M. of 21, 36, 66 = 2772.

Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11

To make it a perfect square, it must be multiplied by 7 x 11.

So, required number = 22 x 32 x 72 x 112 = 213444


Janhavi said: (Oct 1, 2010)  
How come the 2772? Please give me explanation.

Bujji said: (Oct 9, 2010)  
Why should multiplied 7 with 11 ?

Karthik said: (Dec 22, 2010)  
To make it a perfect square
Why should v multipled 7x11 with the lcm ?

Doov said: (Dec 27, 2010)  
Why we should multiply 7 with 11?

Vishal said: (Jan 7, 2011)  
Because 7 and 11 are don't have common factors.

Devi said: (Jan 24, 2011)  
Any shortcut way to find out L.C.M of two or more number.

Neha said: (Feb 2, 2011)  
3|21 36 66
|7 12 22
2|6 11 there fore lcm =3*7*2*6*11=2772
hence these can be written as
3*7*2*2*3*11
here 3 is of two times &2is of two times there fore remaining is 7&11 in order to have all squares 7*11 is taken
ans:213444

Tamil said: (Feb 26, 2011)  
How separate 2772 into 2*2*3*3*7*11?

Nancy said: (Mar 12, 2011)  
I totally cant understand the logic why we have to multiply 7 and 11. Can anyone explain this clearly?

Bilal said: (Mar 22, 2011)  
How should we get to know that we have 2 tak out the lcm of that 3 no.

Anshul said: (Apr 10, 2011)  
How can we know that in which question we have to take lcm or hcf.

Naveen said: (Apr 17, 2011)  
How 7 square and 11 square came in last step please explain?

Sandip said: (Apr 20, 2011)  
2 / 21 36 66
--------------------
2 / 7 18 66
---------------------
3 / 7 9 33
---------------------
3 / 7 3 11
----------------------
/ 7 1 11


2*2*3*3*7*11= 2772


pls see this way solve the problem

Sneha said: (May 18, 2011)  
First least num that is divisible by 21,36,66 by taking l.c.m ,

We get 2772,
by taking factors 2772=2*2*3*3*7*11
as we have find least perfect square
we need to multiply with 7*11,so we can get perfect sq. near to 2772

So the soltn is 2*2*3*3*7*7*11*11 = 213444.

Aandal Priyadarshini said: (Jun 1, 2011)  
Shall we divide it by 2 and 3 either multiplying it by 7 and 11, explain this plz anybody.

Ddamas said: (Jul 9, 2011)  
If we divide it by 2 and 3
The figuers will be 2*3*7*11

And to find it's square root is difficult

If there are words like Highest,Biggest then H.C.F. is to be taken
and if there are words like Smallest,least then L.C.F. is to be taken(though this is not an exact interpretation but it has worked in all cases)

Sangeetha said: (Aug 14, 2011)  
@Sneha

I didn't get last 2 steps in your solution, please can you help me.

Rakhi said: (Aug 27, 2011)  
We should multiple it by 7 and 11 to make it a square... If you can see in the factors that 2*2 * 3*3 *7 * 11 = 2772 can not make a square until we multiply it by 7 to make 7*7 and by 11 to make 11*11.... Now 2*@ *3*3 * 7*7 *11*11 .... all are sqare ..which means (2*3*7*11)2(sqare) - (462)2(sqare) = 213444 (Ans)

Sk K said: (Sep 2, 2011)  
Guys, try to solve such questions by options:


The least perfect square, which is divisible by each of 21, 36 and 66 implies that of all the options correct number should be divisible by 7, 11,2,3.
21=3x7
36=2^2X3^3
66=2x3x11


Of these four options only "1" is divisble by 7.

SO CORRECT ANSWER IS 1.

PS: If there were more than 2 choices divisble by 7, then eliminate one of them by divind them by 11 as well, and so on by the factors of the divisors. It would be your bad luck if you get multiple answers even after eliminating the options..

Raviteja said: (Oct 14, 2011)  
How Separate Into 2 x 2 x 3 x 3 x 7 x 11 The 2772?

Deepu said: (Oct 28, 2011)  
The lcm of 21,36,66=2772

I have a simple method.

213444is divisible by 21 comes 10164
and 36 to comes 5929
and 6 to comes 3234

So finaly it is divisible by 3 numbers.

Sowjanya said: (Oct 28, 2011)  
It is very difficult to divide all the options with the given numbers. It will take more time it is better to go to the LCM/HCF methods. Its very simple that multiplying 7 and 11 to make all the number a perfect square and multiply all the numbers we will get answers.

Kumar said: (Nov 21, 2011)  
How can 22 x 32 x 72 x 112 = 213444 - this be done in less than 10 secs?

Raju Kaki said: (Jan 2, 2012)  
3/21,36,66
2/7,12,22
7,6,11
so l.c.m=3*2*7*6*11
=3^2*2^2*7*11
to make perfect square we have to multiply with 7 and 11the it turns
=3^2*2^2*7^2*11^2

Vijay said: (Jan 31, 2012)  
How can 22*32*72*112 = 213444 this is done in less than 10 sec?

Vks said: (Feb 28, 2012)  
LCM = 2772

REQ TO MULTI 2772*11*7 TO MAKE PERFECT SQR

= 2772*77=213444

Sams said: (Sep 3, 2012)  
21, 36,66 which is divisible by 6
then we have to check hw many answer divisible by 6 and find the least one

Mohit said: (Sep 9, 2012)  
Hey guys its simple. Please refer rakhi's answer. !

Atul said: (Feb 11, 2013)  
2/21,36,66

2/21.18,33

3/21,9,33

3/7,3,11

/7,1,11

So L.C.M : 2*2*3*3*7*11 = 2772.

Sudarshana said: (Jul 29, 2013)  
I found the answer correct when I tried to divide each of the options by 21, 36, 66. And only opt. A was found to divide with all three without any fraction.

Is it the write method ?

Kik Nil88 said: (Sep 26, 2013)  
21 36 66 are divisible by 3.

Now check the options. And then find the least no. Which is also divisible by 3.

Swasthik said: (Oct 10, 2013)  
Hi friends,

Here I will tell you the simple method to solve.

Just add alternative digit from the given answer eg: 213444.

Now add 2+3+4 = 9.

1+4+4 = 9.

Then deduct 9-9=0 if you get answer is 0. That means it is divisible by given number. :).

Uday Kiran said: (Nov 2, 2013)  
The question is " least perfect square which is divisible by each of 21, 36 and 66 ".

So take the LCM of the numbers.

And in the LCM we get 2772.

Which can be written as factors as "2 x 2 x 3 x 3 x 7 x 11".

In which 2 and 3 are double in number but 7 and 11 are singles.

For finding the least perfect square we have to multiply the number by 7 and 11 so that we have all the factors double in number i.e.

"2x2x3x3x7x7x11x11".

Whose multiplied number will be"213444".

Which will be a perfect square.

Pooja said: (Jan 1, 2014)  
Hi @Swasthik.

According to your method 214434 is also a right answer.

Because 214434 now add alternative nos ie 2+4+3 = 9.

1+4+4 = 9 and when we deduct its 0 so it is also a right answer.

Ragu said: (Mar 16, 2014)  
How come the 2772? Please give me explanation.

Saranya said: (Jul 15, 2014)  
Why we should multiply 11*7?

Give any short cut method for lcm.

Balu said: (Jul 17, 2014)  
Why should we do 7*7 and 11*11 at last step?

Agila said: (Jul 27, 2014)  
Guys why we multiply 7 and 11 last step ?

Giftson David said: (Aug 3, 2014)  
How did u get 7^2 and 11^2?
Should have calculated as 2^2 x 3^2 x 7 x 11 right..?

Maha said: (Oct 8, 2014)  
Take LCM for 21, 36 and 66 we get 2*2*3*3*7*11 = 2772,

2 and 3 are came 2 times we will get perfect square so multiply this term with 7*11 so we get 2*2*3*3*7*7*11*11 = 213444.

Santosh said: (Nov 6, 2014)  
Take that example.

Take LCM of that numbers.

LCM (21, 36, 66) = 2*3*7*2*6*11==> 2*3*7*2*3*11==> 2^2*3^2*11*7.

To make above as perfect square we multiply with 11 and 7.

So (2^2*3^2*7*11)*7*11 = 213444.

Tejaswini said: (Nov 7, 2014)  
How it is possible?

Raju said: (Nov 17, 2014)  
2x2x3x3x7x11 = 2772.

Here all are pair numbers but 7 & 11 are single numbers that's why we multiple by 7 & 11 again.

Aditya said: (Dec 10, 2014)  
Example:

3, 9, 21.

Solution: List the prime factors of each.

3:3.
9:3 x 3.
21:3 x 7.

Multiply each factor the greatest number of times it occurs in any of the numbers. 9 has two 3's, and 21 has one 7.

So we multiply 3 two times, and 7 once. This gives us 63, the smallest number that can be divided evenly by 3, 9, and 21.

We check our work by verifying that 63 can be divided evenly by 3, 9, and 21.

Prashant said: (Dec 14, 2014)  
For LCM 21, 36 & 66:

3/21 36 66.

2/7 12 22.

3/7. 6. 11.

2/7. 2. 11.

7. 1. 11.

3 x 3 x 2 x 2 x 7 x 11 = 213444.

Malakarsidda said: (Jan 5, 2015)  
How to sole this step 2772 = 2 x 2 x 3 x 3 x 7 x 11?

Sandeep said: (Jan 17, 2015)  
L.C.M: 21, 36, 66 then we have, 2*2*3*3*7*11.

Now square all these term.

Eg: 4*4*9*9*49*121 = 213444.

Ravi said: (Jan 23, 2015)  
Simply a no is divided by some other nos that nos factor must be divided that no.

Achutha Reddy said: (Jan 29, 2015)  
21 = 3*7.

36 = 3*3*2*2.

66 = 11*3*2.

Means our must be divisible by 2, 3, 7, 11.

**All numbers are evens, so 2 is satisfied.

***3 is common factor for 21, 36, 66 so it is also satisfied.

So you have to check for 7 and 11.

i.e 213444.

S.Manikandan said: (Jun 10, 2015)  
21----7*3.
36-----3*3*2*2.
66-------3*2*11.

So here, [7*3*3*3*2*2*3*2*11].

As per the rule we multiply 7*11*3*3*2*2 = 2772.

Here both 3 and 2 are doubles. For perfect square all should be double. So multiple with 7*11 we get 213444.

Rahul Gupta said: (Jun 17, 2015)  
This solution is very confusing, kindly explain in simple manner.

Sheikh Muhammad Ammar said: (Jun 18, 2015)  
I think according to maths rule 7 & 11 must be multiplied on both ends.

Hence 2^2*3^2*7*11*(7*11) = 2772*7*11.

= 2^2*3^2*7^2*11^2 = 213444.

Raaj said: (Jul 21, 2015)  
How the answer come like this?

Yash said: (Sep 17, 2015)  
We divide all answer option by 21, 36, 66 and find a option.

Gaurav said: (Nov 20, 2015)  
Can't understand how 7*11 is considered and what about 2*2 & 3*3?

Ravinesh Kumar said: (Dec 11, 2015)  
I am not satisfy with this solution.

Ravinesh Kumar said: (Dec 11, 2015)  
This solution is not satisfactory.

Yassmin said: (Mar 18, 2016)  
A square number is when you times a number or numbers to itself.

Harish said: (Apr 20, 2016)  
Is there any other method to solve the question? If yes please tell me the trick.

Ganesh Policherla said: (Jun 14, 2016)  
We can get the perfect square must multiplied 7 x 11.

Mz Gucchi said: (Jun 17, 2016)  
Remember it's the least common factor we looking for 21, 36 and 66.

Find the Lcm = 3 * 2 * 7 * 6 * 11 = 3 * 2 * 7 * 3 * 2 * 11 = 2772 (the 3*2 after 7 is a perfect square to replace the 6 that's in the initial equation coz 3*2 is 6).

3 and 2 are the highest common factors while 7 and 11 are the least because they both appear once. So multiply the Lcm (2772) with 7 and 11 and you get your answer;
That is 2772 * 7 * 11 = 213444.

Hope this helped someone understand better.

K.Viji said: (Jul 15, 2016)  
Why multiplied by 7x11?

Neelraj said: (Jul 24, 2016)  
It is multiplied by 7 so that we get 7^2 and 11 because we get 11^2. So perfect square is obtained.

Logapriya said: (Sep 2, 2016)  
Please anyone explain in simple way.

Najeeb said: (Oct 5, 2016)  
How to find out least perfect square?

Nick said: (Jan 6, 2017)  
How to find out LCM? Someone help me.

Aadal said: (May 7, 2017)  
Hi, @Nick! this is the way to take out lcm.

Suppose the number is 27 now,
27will not go with 2 but with 3 so we'll divide it with 3 as follow.
3/27
3/9
3/3
=1
So lcm =3*3*3.

So, in nutshell, we have to take a least no divisible by the given no and then whatever the quotient comes write it in the next line and then again divide that no divisible by least no and then the process continues until you get 1 at last keep solving and in the end write all the multiples together.

Shudhakar Kumar Gupta said: (Jul 9, 2017)  
7and 11 multiply because according to question make perfect square 2 and 3 is left square but 7 and 11 not a perfect square so 7and 11 make a perfect square so multiply 7 and 11.

Anomi said: (Sep 3, 2017)  
21 is having a factor as 7 and 3.
So check each option whether it is divisible by 7 or not.
So option a is only divisible by 7.

Madhu said: (May 30, 2018)  
| 21 36 66
2| 21 18 33
2| 21 9. 33
3| 7. 3. 11.

==> 2*2*3*3*7*11.
=> 4*9*77,
=> 36*77,
=> 2772.

To make perfect square means, Make all digits square.

Already we have a square for 2 and 3,
Remaining make square i.e., 7^2. 11^2,

So, Totally....2772*11*7=213444.

Laxmi said: (Jun 3, 2018)  
Why should we multiply by 7 and 11? Please tell me.

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