Aptitude - Square Root and Cube Root - Discussion
Discussion Forum : 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:
Answer: Option
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
Discussion:
80 comments Page 2 of 8.
Sowjanya said:
1 decade ago
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.
Sneha said:
1 decade ago
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.
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.
Swasthik said:
1 decade ago
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. :).
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. :).
Sandip said:
1 decade ago
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
--------------------
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
Achutha reddy said:
1 decade ago
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.
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:
1 decade ago
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.
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.
Santosh said:
1 decade ago
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.
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.
Pooja said:
1 decade ago
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.
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.
Sudarshana said:
1 decade ago
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 ?
Is it the write method ?
Shudhakar kumar gupta said:
8 years ago
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.
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