Question

Find the smallest four digit number that leaves reminder 7 when divided with 12,15,18​

Answer 1

Answer:

n=16a+8  

n=18b+8  

Lets rearrange the equation for further convenience. You’ll figure out why it is needed.

n−8=16a  

n−8=18b  

From the rearranged equations it can be inferred that  n−8  is divisible by both  16  and  18 . This doesn’t happen unless  n−8  is a multiple of  LCM  of  16  and  18 .

LCM  of  16  and  18 , gives us second such number (read  n− 8), which is divided by both  16  and  18 . [First such number is  0  itself.]

We know that  LCM(16,18)=144 , which is nothing but  n−8  as per our discussion, giving us  n  as  152 .

We can recheck the conditions given in the question. Reminder when  152  is divided by  16  and  18  is indeed  8 .

Since this is a  3−digit  number,  152  is the not the number we are looking for.

Explanation:

Answer 2

The required number is 1011.

Please drop her I'd...