Question

find the smallest number which when increased by 3 is divisible by 21 28 36 and 45

Answer 1

Consider the number : X

→ ( X + 3 ) is divisible by : 21 , 28 , 36 , 45

=> ( X + 3 ) has all factors of : 21 , 28 , 36 , 45
=> ( X + 3 ) is divisible by  : LCM( 21 , 28 , 36 , 45 )

=> ( X + 3 ) is divisible by : 36 x 7 x 5 = 36 x 35 = 1260

=> X = ( 1260k - 3 )

=>Smallest such number = - infinity 

However, smallest such number in the NATURAL NUMBER set is 
               = ( 1260 x 1 - 3 ) = 1257  [ the desired number ]