Question

The least number which when divided by 16,18,20,and 25 leaves 4 as remainder in each case but when divided by 7 leaves no remainder​

Answer 1

Answer:LCM of 16, 18, 20, 25  =   lcm of  2^4 ,  2 * 3^2,   2^2 * 5, 5 * 5

              = 2^4 * 3^2 * 5 * 5 = 3, 600

so the number N = 3, 600 * x + 4,  

               3, 600 * x + 4 = 7 * y            ,  x and y are positive integers

 

         y =  514 x + 2x/7 + 4/7  

 

         as y is an integer,   2x+4 = multiple of 7.  

 

       smallest such number is  x = 5

 

       Hence the number N = 3, 600 * 5 + 4 = 18, 004

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