How many positive integers less than or equal to 6000 are no

How many positive integers less than or equal to 6000 are not multiples of 4,5,6 and 7?

Solution

Given below or equal to 6000.

multiples of all 4 and 5 and 6 and 7.

                   LCM of4,5,6,7=420

     multiples of 420 below or equal to 6000.

                            =14

so, total no of positive integers less then or equal to 6000 not multiples of 4 and 5 and 6 and 7.

                          =6000-14

                          =5986.

   Ans:5986