Find-the-greatest-four-digit-number-which-when-divided-by-18-and-12-leaves-a-remainder-of-4-in-each-case-

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

Find the greatest four digit number

which when divided by 18 and 12

leaves a remainder of 4 in each case

Answered by tanmay last updated on 14/May/19

L C M o f 18 a n d 12 = 36

\frac{9999}{36} = 277 + \frac{27}{36}

n o w 277 \times 36 = 9972

s o r e q u i r e d a n s i s 9972 + 4 = 9976

c o r r e c t e d \dots

T h a n k y o u M j s s i r

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

b u t t h e a n s w e r i s g i v e n 9976

Commented by MJS last updated on 13/May/19

just a typo ?

3^{rd} line must be

277 \times 36 = 9972 \Rightarrow 9972 + 4 = 9976

Answered by MJS last updated on 13/May/19

\mod (9999, 18) = 9

\mod (9999, 12) = 3

18 ∣ (9999 - 9 - 18 m)

12 ∣ (9999 - 3 - 12 n)

- 9 - 18 m = - 3 - 12 n

n = \frac{3 m + 1}{2}

\Rightarrow m = 1 \land n = 2

18 ∣ 9972

12 ∣ 9972

\Rightarrow searched number is 9976

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