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Question
The greatest four digit number which when divided by 18 and 12 leaves a remainder of 4 in each case is
(a) 9976
(b) 9940
(c) 9904
(d) 9868
(a) 9976
(b) 9940
(c) 9904
(d) 9868
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Solution
18 = 1 × 2 × 3 × 3 = 21 × 32
12 = 1 × 2 × 2 × 3 = 22 × 31
LCM of 18 and 12 = 22 × 32 = 36
Largest 4-digit number is 9999
Now, if we divide 9999 by 36, we will get 277.75 as quotient.
The integer just less than 277.75 is 277
∴ Required number = (36 × 277) + 4 = 9972 + 4 = 9976
Hence, the correct answer is option (a).
12 = 1 × 2 × 2 × 3 = 22 × 31
LCM of 18 and 12 = 22 × 32 = 36
Largest 4-digit number is 9999
Now, if we divide 9999 by 36, we will get 277.75 as quotient.
The integer just less than 277.75 is 277
∴ Required number = (36 × 277) + 4 = 9972 + 4 = 9976
Hence, the correct answer is option (a).
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