The least perfect square, which is divisible by each of 20, 35 and 65 is
Answers
Answer:
the correct or perfect answer is 1
Answer:
The least perfect square, which is divisible by each of 20, 35, and 65 =828100
Step-by-step explanation:
Given numbers are 20,35,65
To find,
Least perfect square divisible by each of the given numbers
Solution:
The least number which is divisible by the given numbers is the LCM of the numbers
To find LCM of 20,35,65
Prime factorization of 20 = 2×2×5
Prime factorization of 35 = 7×5
Prime factorization of 65 = 13×5
LCM(20,35,65) = 2×2×5×7×13 = 1820
We know that all the multiples of the LCM are also divisible by the given three numbers
Since 1820 = 2²×5×7×13, the least number to be multiplied to make 1820 a perfect square is 5×7×13 = 455
1820×455 =828100
That is, 828100 is the least multiple of 1820 which is a perfect square.
Hence the least perfect square which is divisible by each of 20,35,95 = the Least multiple of 1820 which is the square number = 828100
∴The least perfect square, which is divisible by each of 20, 35, and 65 =828100
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