Find the maximum three digit number divided by 12 by 11 and 18 by 17

12m+11=18n+17 m, n is a positive integer.

12m-18n=6

2m-3n=1

A maximum three-digit number is required.

18n+17<1000

n《i.e., n is a positive integer less than or equal to 54.

If n=54 and m is not an integer, round it off.

If n=53 and m=80, it is true.

Therefore, 12 80 + 11 = 971 is this appropriate number.

Find the three digits with the highest common multiple of 12 and 18, and subtract one.

Then 216*4=864,864-1=863

Then the maximum three-digit number divided by 12 by 11 and 18 by 17 is 863

1 is divisible by 12 and 18, with the minimum being 72-1=71

The maximum three-digit number is 936-1=935

You can do this 12*18, and then you see how many times the difference from 1000 is closer.

So *5 = 1080, then subtract their least common multiple 36 until it is less than 1000, and then subtract 1 = 971

None of the above methods are correct.

Set to x, by the question, x=12m+11=18n+17

then 2m=3n+1

m=(3n+1)/2

To make m a positive integer, n can only take odd numbers: 1, 3, 5, ,......Thus x is the largest three-digit number, and only the maximum odd number n satisfying the inequality of 18n+17<=999 is required, and the solution is n<, so n=53

At this point, 18n+17=971

It's 971. First divide 999 by 18 to get 55, (55-1)*18+17 to get more than 999, is excluded, so 53*18+17=971, set in the division of 12 and 11 is also valid.

The number 140 is divisible by 7 and 2, divisible by 5 and 2, and 13 divisible by 10.

Summary. The maximum number is likely to be 2767. Depending on the remainder, the six-digit number could be 2727, 2733, 2737, 2743, 2747, 2753, 2757, 2763 or 2767, and the largest of these numbers is 2767.

Example 1A six-digit number 2727 is divided by 3 by 1, and 9 is divided by 4, the largest number is pro, are you this a complete topic.

This Sen modulus is likely to be 2767 at most. According to the remainder, the six-digit number could be 2727, 2733, 2737, 2743, 2747, 2753, 2757, 2763 or 2767, and the largest of these numbers is 2767.

If you want to know what the maximum number is, it is actually calculated according to the divisor and the dividend. Finally add quotient. You can get this number, and then sort it according to the size, and stare at it to get the largest number.

The remainder is the divisor, so the remainder is up to 24 and the dividend is up to 25 11+24 299.

The remainder is maxed out at 11, so the dividend is 12 * 11 + 11 = 143

Only the minimal. Except for the number of bright finches, the number is greater than the remainder.

So the minimum belief is 4

So the minimum dividend cruise is 18 4 + 3 = 75

The remainder is the most knowledgeable type: 7-1=6,7 12+6

Answer: The dividend is 90 when the remainder is the largest

So the answer is: 90 Guess what's wrong.

The maximum remainder is 12. The dividend is 45x13 585 ten 12 597

<> the maximum number of the four prudent checks that meet the requirements is: 9305 verification wide wheel: