The least number which when divided by 6, 9, | vedclass

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(B) To find the least number that leaves a remainder of $2$ when divided by $6, 9, 12, 15,$ and $18$,we first find the Least Common Multiple $(LCM)$ o

Vedclass · Accepted Answer

$182$

Vedclass · Answer

(B) To find the least number that leaves a remainder of $2$ when divided by $6, 9, 12, 15,$ and $18$,we first find the Least Common Multiple $(LCM)$ of these numbers.Prime factorization:$6 = 2 	imes 3$$9 = 3^2$$12 = 2^2 	imes 3$$15 = 3 	imes 5$$18 = 2 	imes 3^2$$LCM = 2^2 	imes 3^2 	imes 5 = 4 	imes 9 	imes 5 = 180$.Since the number must leave a remainder of $2$ in each case,we add the remainder to the $LCM$.Required number $= LCM + 2 = 180 + 2 = 182$.

The least number which when divided by $6, 9, 12, 15, 18$ leaves the same remainder $2$ in each case is

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