To find the number of positive integers less than 200 that are divisible by 2, 3, and 5, we need to find the least common multiple (LCM) of these three numbers.
The LCM of 2, 3, and 5 is given by:
LCM(2, 3, 5) = 2 × 3 × 5 = 30
The positive integers less than 200 that are divisible by 30 will be multiples of 30. To find how many multiples of 30 are less than 200, we can divide 200 by 30 and round down to the nearest whole number:
200 ÷ 30 ≈ 6.6667
Rounding down, we get 6.
Therefore, there are 6 positive integers less than 200 that are divisible by 2, 3, and 5.