How many positive integers under 50 are multiples of neither 4 nor 6

Candidates range from 1 to 50.

50/4=12 positive integers are multiples of 4

50/6=8 positive integers are multiples of 6

50/12=4 positive integers are multiples of 12 (LCM of 4 and 6)

By the inclusion/exclusion principle, the number of multiples of either 4 or 6 is equal to 12+8-4=16.

Therefore, the complement is the number of positive integers that are multiples of neither 4 nor 6 = 50-16=34.