How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

Question

Accepted Answer

41. The number of multiples of 2 between 1 and 120 = 60 The number of multiples of 5 between 1 and 120 which are not multiples of 2 = 12 The number of multiples of 7 between 1 and 120 which are not multiples of 2 and 5 = 7 Hence, number of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7