Find the smallest number of five digits exact | vedclass

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Question

(C) The smallest five-digit number is $10000$.First,find the $LCM$ of $12, 16, 18$ and $27$:$12 = 2^2 	imes 3$$16 = 2^4$$18 = 2 	imes 3^2$$27 = 3^3$

Vedclass · Accepted Answer

$10368$

Vedclass · Answer

(C) The smallest five-digit number is $10000$.First,find the $LCM$ of $12, 16, 18$ and $27$:$12 = 2^2 	imes 3$$16 = 2^4$$18 = 2 	imes 3^2$$27 = 3^3$$LCM = 2^4 	imes 3^3 = 16 	imes 27 = 432$.Now,divide $10000$ by $432$ to find the remainder:$10000 \div 432 = 23$ with a remainder of $64$.To find the smallest five-digit number exactly divisible by $432$,we subtract the remainder from the divisor and add it to the smallest five-digit number:Required number $= 10000 - 64 + 432 = 10368$.

Find the smallest number of five digits exactly divisible by $12, 16, 18$ and $27$.

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