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(D) To find the smallest five-digit number divisible by $15$,$55$,and $99$,we first find the Least Common Multiple $(LCM)$ of these numbers.Step $1$:

Vedclass · Accepted Answer

$10395$

Vedclass · Answer

(D) To find the smallest five-digit number divisible by $15$,$55$,and $99$,we first find the Least Common Multiple $(LCM)$ of these numbers.Step $1$: Prime factorization of the numbers:$15 = 3 	imes 5$$55 = 5 	imes 11$$99 = 3^2 	imes 11$Step $2$: Calculate the $LCM$ by taking the highest power of each prime factor present:$LCM(15, 55, 99) = 3^2 	imes 5 	imes 11 = 9 	imes 5 	imes 11 = 495$.Step $3$: The smallest five-digit number is $10000$.Divide $10000$ by $495$:$10000 \div 495 = 20.202...$Step $4$: To find the smallest five-digit multiple,we take the next integer quotient,which is $21$.$495 	imes 21 = 10395$.Thus,the smallest five-digit number divisible by $15$,$55$,and $99$ is $10395$.

Find the smallest five-digit number which is exactly divisible by $15$,$55$,and $99$.

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