Question

Find the least number which when divided by 9 , 11 and 13 leaves 1, 3, 5 as the respective remainders. easy method please dont copy from google or any other website

Answer 1

Given : 9, 11 and 13 leaves 1,3 , 5 as the respective remainders.

To find : Find the least number which when divided by 9, 11 and 13 leaves 1, 3 and 5 as the respective remainders.

solution : here you see,

9 - 1 = 8

11 - 3 = 8

13 - 5 = 8

so, required number is LCM{9, 11, 13} - 8

= 1287 - 8

= 1279

verification : 1279/9 ⇒remainder = 1

1279/11 ⇒remainder = 3

1279/13 ⇒remainder = 5

Therefore it is clear that 1279 is the smallest number which when divided by 9, 11, 13 leaves 1, 3 , 5 as the respective remainders .