Question : What is the greatest number of six digits, which when divided by each of 16, 24, 72, and 84 leaves the remainder 15?
Option 1: 999981
Option 2: 999951
Option 3: 999963
Option 4: 999915
Correct Answer: 999951
Solution :
The least common multiple (LCM) of 16, 24, 72, and 84 is 1008.
The greatest six-digit number is 999999.
The greatest number less than 999999 which is divisible by 1008 is given by dividing 999999 by 1008 and taking the round down to the nearest whole number, then multiplying by 1008.
This gives us 999936, which is the greatest six-digit number divisible by 1008.
Finally, we add 15 to this number (since we want the number to leave a remainder of 15 when divided by 16, 24, 72, and 84), giving us 999951.
Hence, the correct answer is 999951.
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