Question

A number when divided by 11, 13 and 17 leaves a remainder of 7,9 and 13 respectively. find the smallest such 4 digit no

Answer 1

Answer:

Observe that

11 - 7 = 13 - 9 = 17 - 13 = 4

So smallest number will be

= LCM( 11 , 13 ,17 ) - 4

= 2431 - 4

= 2427

Answer 2

The smallest such 4 digit number is 2427.

Given:-

Numbers are = 11, 13, 17

Remainder = 7, 9, 13

To Find:-

The smallest such 4 digit number.

Solution:-

We can simply find the the smallest such 4 digit number by following these simple steps.

As,

Numbers are = 11, 13, 17

Remainder = 7, 9, 13

According to the formula,

Actual 4 digit number = LCM - difference

Now,

LCM of the Numbers = 11*13*17

LCM = 143*17

LCM = 2431

And the difference between numbers and their remainders =

11-7 = 4

13-9 = 4

17-13 = 4

So, the Actual 4 digit number = LCM - difference

$number(n) = 2431 - 4$

$n = 2427$

Hence, The smallest such 4 digit number is 2427.

#SPJ2