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Question Number 59714 by Khairun Nisa last updated on 13/May/19

$$\mathrm{Find}\mathrm{the}\mathrm{greatest}\mathrm{four}\mathrm{digit}\mathrm{number}$$$$\mathrm{which}\mathrm{when}\mathrm{divided}\mathrm{by}18\mathrm{and}12$$$$\mathrm{leaves}\mathrm{a}\mathrm{remainder}\mathrm{of}4\mathrm{in}\mathrm{each}\mathrm{case}$$

Answered by tanmay last updated on 14/May/19

$$$$$$$$$$LCMof18and12=36$$$$\frac{9999}{36}=277+\frac{27}{36}$$$$now277\times 36=9972$$$$sorequiredansis9972+4=9976$$$$corrected...$$$$ThankyouMjssir$$

Commented by Khairun Nisa last updated on 13/May/19

$$buttheanswerisgiven9976$$

Commented by MJS last updated on 13/May/19

$$\mathrm{just}\mathrm{a}\mathrm{typo}?$$$$3^{\mathrm{rd}}\mathrm{line}\mathrm{must}\mathrm{be}$$$$277\times 36=9972\Rightarrow 9972+4=9976$$

Answered by MJS last updated on 13/May/19

$$\mathrm{mod}(9999,18)=9$$$$\mathrm{mod}(9999,12)=3$$$$18\mid (9999-9-18m)$$$$12\mid (9999-3-12n)$$$$-9-18m=-3-12n$$$$n=\frac{3m+1}{2}$$$$\Rightarrow m=1\wedge n=2$$$$18\mid 9972$$$$12\mid 9972$$$$\Rightarrow \mathrm{searched}\mathrm{number}\mathrm{is}9976$$

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