The least perfect square number which is divi | vedclass

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(D) To find the least perfect square number divisible by $3, 4, 5, 6$,and $8$,we first find their Least Common Multiple $(LCM)$.$\begin{array}{c|ccccc

Vedclass · Accepted Answer

$3600$

Vedclass · Answer

(D) To find the least perfect square number divisible by $3, 4, 5, 6$,and $8$,we first find their Least Common Multiple $(LCM)$.$\begin{array}{c|ccccc} 2 & 3, & 4, & 5, & 6, & 8 \ \hline 2 & 3, & 2, & 5, & 3, & 4 \ \hline 3 & 3, & 1, & 5, & 3, & 2 \ \hline & 1, & 1, & 5, & 1, & 2 \end{array}$$LCM = 2 	imes 2 	imes 3 	imes 5 	imes 2 = 120$.Prime factorization of $120 = 2^3 	imes 3^1 	imes 5^1$.For a number to be a perfect square,the exponent of each prime factor must be even. To make $120$ a perfect square,we multiply it by the factors needed to make the exponents even: $2^1 	imes 3^1 	imes 5^1 = 30$.Required number $= 120 	imes 30 = 3600$.

The least perfect square number which is divisible by $3, 4, 5, 6$ and $8$ is:

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