A number which is multiple of 11 leaves a remainder 1 when it is divided by 123456. What is the number?

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Solution

Let the number be x which when divided by 123456, we get remainder as 1.
Then, 123456 is also the multiple of (x-1).
And, 11 is a multiple of x.

So to get the value of x,
we first divide 123456 by 11 to get remainder = 3

Now, if we multiply 3 with the least number (i.e. 4) so as to get a number (i.e. 12) which when divided by 11, we get remainder as 1.

So, the required least number which satisfies your conditions is = $123456 \times 4 = 493824$

By the way this is a good question but it is of higher standard.

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