The least perfect square, which is divisible by each of 21, 36 and 66 is:
A. 213444
B. 214344
C. 214434
D. 231444
A?
That's what I get.
The LCM of 21,36,66 = 2^2 * 3^2 * 7 * 11
so, you need an extra 7*11 to get a perfect square. A.
First we have to find L.C.M. of all numbers:
21=3*7
36=2*2*3*3
66=2*3*11
The L.C.M. =2*3*2*3*7*11
=2^2*3^2*7*11
For perfect square of all numbers, we need perfect square of 7and 11:
=7^2*11^2
The answer=4*9*49*121 =213444
If you want one more process for solving this question, I will help you.
Thanks
To find the least perfect square that is divisible by each of the given numbers (21, 36, and 66), we need to find the LCM (Least Common Multiple) of these numbers.
Step 1: Prime factorize each number.
21 = 3 × 7
36 = 2^2 × 3^2
66 = 2 × 3 × 11
Step 2: Take the highest power of each prime factor in the given numbers.
- The highest power of 2 is 2^2.
- The highest power of 3 is 3^2.
- The highest power of 7 is 7.
- The highest power of 11 is 11.
Step 3: Multiply these highest powers together to get the LCM.
LCM = 2^2 × 3^2 × 7 × 11 = 4 × 9 × 7 × 11 = 2772
Therefore, the least perfect square that is divisible by each of 21, 36, and 66 is 2772^2.
Now let's check the options:
A. 213444: Not divisible by 21, 36, or 66.
B. 214344: Not divisible by 21, 36, or 66.
C. 214434: Not divisible by 21, 36, or 66.
D. 231444: Not divisible by 21, 36, or 66.
None of the options are divisible by 21, 36, or 66, so the correct answer cannot be determined from the given options.
The correct answer is not A.