SOLUTION: Find the greatest number of 6 digit dividing by 15,18,21,24,27 leaves the remainder 10,13,16,19,and 22.

Question 768603: Find the greatest number of 6 digit dividing by 15,18,21,24,27 leaves the remainder 10,13,16,19,and 22.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The remainders are always 5 short of the divisor.
For example, if the number, is divided by 15, the remainder is , so that for some integer ,
-->,
which makes a multiple of .
The same happens with 18, 21, 24, and 27.
That number, , is such that is a multiple of 15, 18, 21, 24, and 27.
That means is a multiple of the least common multiple of
,
,
,
, and
,
and that least common multiple is

Dividing 1,000,000 by 7560 we find a quotient of 132 plus a remainder of 2080.
That means that -->
and 997,920 is a multiple of 7560.
The next multiple of 7560 is
That means that is the largest multiple of 15, 18, 21, 24, and 27 that will yield a number with 6 digits,
So --> .

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