What least number must be subtracted from 129 | vedclass

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(B) To find the number that leaves a remainder of $6$ when divided by $9, 11,$ and $13$,we first calculate the Least Common Multiple $(LCM)$ of $9, 11

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(B) To find the number that leaves a remainder of $6$ when divided by $9, 11,$ and $13$,we first calculate the Least Common Multiple $(LCM)$ of $9, 11,$ and $13$.Since $9, 11,$ and $13$ are coprime,their $LCM = 9 	imes 11 	imes 13 = 1287$.$A$ number that leaves a remainder of $6$ when divided by $9, 11,$ and $13$ is of the form $(LCM + 6) = 1287 + 6 = 1293$.We need to subtract a number from $1294$ to get $1293$.Required number $= 1294 - 1293 = 1$.

What least number must be subtracted from $1294$ so that the remainder when divided by $9, 11, 13$ will leave in each case the same remainder $6$?

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