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Question Number 113508 by Lekhraj last updated on 13/Sep/20

Commented by mr W last updated on 13/Sep/20

$$igotN=LCM(5,7,8,9)=2520$$

Commented by Rasheed.Sindhi last updated on 13/Sep/20

$$N=252$$

Answered by Rasheed.Sindhi last updated on 13/Sep/20

$$10\mathrm{N}+1\equiv 0\left(mod1\right)$$$$Norestrictionon\mathrm{N}$$$$10\mathrm{N}+2\equiv 0\left(mod2\right)$$$$Norestrictionon\mathrm{N}$$$$10\mathrm{N}+3\equiv 0\left(mod3\right)$$$$\Rightarrow 3\mid \mathrm{N}$$$$10\mathrm{N}+4\equiv 0\left(mod4\right)$$$$\Rightarrow 2\mid \mathrm{N}$$$$10\mathrm{N}+5\equiv 0\left(mod5\right)$$$$Norestrictionon\mathrm{N}$$$$10\mathrm{N}+6\equiv 0\left(mod6\right)$$$$\Rightarrow 3\mid \mathrm{N}$$$$10\mathrm{N}+7\equiv 0\left(mod7\right)$$$$\Rightarrow 7\mid \mathrm{N}$$$$10\mathrm{N}+8\equiv 0\left(mod8\right)$$$$\Rightarrow 4\mid \mathrm{N}$$$$10\mathrm{N}+9\equiv 0\left(mod9\right)$$$$\Rightarrow 9\mid \mathrm{N}$$$$HenceNistheleastnumber$$$$whichisdivisibleby2,3,4,7\mathrm{\&}9$$$$\mathrm{N}=\mathrm{LCM}(2,3,4,7,9)$$$$=\mathrm{LCM}(4,7,9)=252$$

Commented by mr W last updated on 13/Sep/20

$$nicesolutionsir!$$

Commented by Rasheed.Sindhi last updated on 14/Sep/20

$$\mathcal{T}hanks\mathit{s}\mathit{i}\mathit{r}!$$

Commented by Lekhraj last updated on 14/Sep/20

$$T\mathrm{hanks}\mathrm{sir}\mathrm{for}\mathrm{correction}$$

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