The least perfect square,which is divisible b | vedclass

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(A) To find the least perfect square divisible by $21, 36$,and $66$,we first find their Least Common Multiple $(LCM)$.Prime factorization of the numbe

Vedclass · Accepted Answer

$213444$

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(A) To find the least perfect square divisible by $21, 36$,and $66$,we first find their Least Common Multiple $(LCM)$.Prime factorization of the numbers:$21 = 3 	imes 7$$36 = 2^2 	imes 3^2$$66 = 2 	imes 3 	imes 11$$LCM$ $= 2^2 	imes 3^2 	imes 7 	imes 11 = 4 	imes 9 	imes 77 = 2772$.For a number to be a perfect square,the exponent of each prime factor in its prime factorization must be even.In the $LCM$ $(2^2 	imes 3^2 	imes 7^1 	imes 11^1)$,the prime factors $7$ and $11$ have odd exponents.To make it a perfect square,we must multiply the $LCM$ by $7 	imes 11 = 77$.Required perfect square $= 2772 	imes 77 = 213444$.

The least perfect square,which is divisible by $21, 36$ and $66$ completely is

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