Calculations based on HCF and LCM - Find the largest and smallest number of n digits exactly divisible by a series of n numbers and also find the greatest and smallest number which leaves a remainder r when divided with this series.

Largest number of N digits exactly divisible by a series of N numbers

Steps:

1. Find largest number of N digits.
2. Find lcm of N numbers.
3. Find remainder (largest of N digits) % (lcm of N numbers).
4. Required number is (Largest number) - (remainder) 

Smallest number of N digits exactly divisible  by a series of N numbers.

Steps:

1. Find smallest number of N digits.
2. Find lcm of N numbers.
3. Find remainder (smallest number) %(lcm of N numbers ).
4. Required number is (smallest number )+ (lcm of N number - remainder).

To find greatest number which on dividing with a series of N numbers leaves remainders R1,R2,......Rn respectivelly.

Steps: 

1. Subtract N^th number with its respective remainder, i,e (N1 - R1) , (R2 - R2) ,........ ,(Nn-Rn).
2. Find the HCF of the above obtained series i.e HCF of (N1-R1) , (N2 - R2), ....., (Nn-Rn)

To find least number which when divided by a series of N numbers leaves a remainder R

Step:

1. Find LCM of N numbers 
2. LCM + R.