Question

The smallest 4 digit number such that when is divided by 12 18 21 and 28 it leaves remainder 3 in each case

Answer 1

Answer:1011

Step-by-step explanation:

Let m be the required number. then m leaves a remainder of 3 when divided by 12, 18, 21, and 24

So m-3 will be a multiple od 12, 18, 21 and 24

12=2x2x3

18=2x3x3

21=3x7

24=2x2x2x3

So LCM= 2x2x3x3x7x2=504

Smallest 4 digit number is 1000 which when divided by 504 leaves a remainder of 496

So the smallest four digit number which is a multiple of 504 is

1000+(504-496)=1008

So m-3=1008

m= 1011