Question

Which is the least number, which, when divided by 12 and 16, leave the same remainder, but is exactly divisible by 11?

Answer 1

Hey Mate

Here is your answer

962 is the least number, which, when divided by 12 and 16, leave the same remainder and is exactly divisible by 11

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Answer 2

Given :

A number when divided by 12 and 16 leaves the same remainder and is exactly divisible by 11.

To Find :

Least number which follows the above given statement

Solution:

Let thee number be n

Whenever  we get the questions to find least numbers which leaves same remainder after divided by 2 numbers

always calculate the LCM of the two numbers.

Lowest common multiple of both the numbers is 48.

the number is exactly divisible by 11. Hence find the nearest number to 48 which is divisible by 11.

the number is 55

55 when divided by 12 leaves 7 as remainder.

Similarily when 55 is divided by 16 leaves 7 as remainder

Hence the least number when divided by 12 and 16 leaves the same remainder and is exactly divisible by 11 is 55.