Find the greatest number of five digits which | vedclass

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(B) Step $1$: Find the $L.C.M.$ of $8, 9$ and $10$.$8 = 2^3$$9 = 3^2$$10 = 2 	imes 5$$L.C.M. = 2^3 	imes 3^2 	imes 5 = 8 	imes 9 	imes 5 = 360$.S

Vedclass · Accepted Answer

$99723$

Vedclass · Answer

(B) Step $1$: Find the $L.C.M.$ of $8, 9$ and $10$.$8 = 2^3$$9 = 3^2$$10 = 2 	imes 5$$L.C.M. = 2^3 	imes 3^2 	imes 5 = 8 	imes 9 	imes 5 = 360$.Step $2$: Find the greatest $5$-digit number,which is $99999$.Step $3$: Divide $99999$ by $360$ to find the remainder.$99999 \div 360 = 277$ with a remainder of $279$.Step $4$: Subtract the remainder from the greatest $5$-digit number to find the largest number divisible by $360$.$99999 - 279 = 99720$.Step $5$: Add the required remainder $(3)$ to this number.$99720 + 3 = 99723$.Therefore,the required number is $99723$.

Find the greatest number of five digits which when divided by $8, 9$ and $10$ leaves $3$ as a remainder in each case.

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