Find the least number of five digits which wh | vedclass

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(C) First, observe the difference between the divisors and their respective remainders:$8 - 1 = 7$$12 - 5 = 7$$16 - 9 = 7$$20 - 13 = 7$The common diff

Vedclass · Accepted Answer

$10073$

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(C) First, observe the difference between the divisors and their respective remainders:$8 - 1 = 7$$12 - 5 = 7$$16 - 9 = 7$$20 - 13 = 7$The common difference is $7$.Next, find the $L.C.M.$ of $8, 12, 16$ and $20$:$8 = 2^3$$12 = 2^2 	imes 3$$16 = 2^4$$20 = 2^2 	imes 5$$L.C.M. = 2^4 	imes 3 	imes 5 = 16 	imes 15 = 240$.The smallest five-digit number is $10000$.Divide $10000$ by $240$:$10000 \div 240 = 41$ with a remainder of $160$.The smallest five-digit number exactly divisible by $240$ is $10000 + (240 - 160) = 10080$.The required number is $(L.C.M. 	ext{ of divisors}) - (	ext{common difference}) = 10080 - 7 = 10073$.

Find the least number of five digits which when divided by $8, 12, 16$ and $20$ leaves remainders $1, 5, 9$ and $13$ respectively.

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