The least number which when divided by 12, 15 | vedclass

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(D) To find the least number that leaves a remainder of $8$ when divided by $12, 15, 20$ and $54$, we first find the Least Common Multiple $(LCM)$ of

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$548$

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(D) To find the least number that leaves a remainder of $8$ when divided by $12, 15, 20$ and $54$, we first find the Least Common Multiple $(LCM)$ of these numbers.$\begin{array}{r|rrrr} 2 & 12, & 15, & 20, & 54 \ \hline 2 & 6, & 15, & 10, & 27 \ \hline 3 & 3, & 15, & 5, & 27 \ \hline 3 & 1, & 5, & 5, & 9 \ \hline 5 & 1, & 1, & 1, & 3 \end{array}$$LCM = 2 	imes 2 	imes 3 	imes 3 	imes 5 	imes 3 = 540$.The required number is $LCM + 	ext{remainder} = 540 + 8 = 548$.

The least number which when divided by $12, 15, 20$ and $54$ leaves in each case a remainder of $8$ is:

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