Find the least number which when decreased by | vedclass

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Question

(C) To find the least number that satisfies the condition,we first need to find the Least Common Multiple $(LCM)$ of the given numbers: $14, 15, 21, 3

Vedclass · Accepted Answer

$3371$

Vedclass · Answer

(C) To find the least number that satisfies the condition,we first need to find the Least Common Multiple $(LCM)$ of the given numbers: $14, 15, 21, 32, 60$.Prime factorization:$14 = 2 	imes 7$$15 = 3 	imes 5$$21 = 3 	imes 7$$32 = 2^5$$60 = 2^2 	imes 3 	imes 5$$LCM = 2^5 	imes 3 	imes 5 	imes 7 = 32 	imes 15 	imes 7 = 480 	imes 7 = 3360$.The problem states that the number,when decreased by $11$,is divisible by these numbers. This means the required number is $LCM + 11$.Required number $= 3360 + 11 = 3371$.

Find the least number which when decreased by $11$ is divisible by $14, 15, 21, 32$ and $60$.

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