How many of the first 500 positive integers are divisible by 3, 4 and 5?

The least common multiple of 3,4, and 5 is the smallest integer that is also divisible by 3,4, and 5. Because 3,4, and 5 do not share any common factors, the least common multiple can be determined by finding the product of 3,4, and 5. 

\(3*4*5=60\)

All multiples of 60 bounded between 1 and 500 are the only integers that satisfy the original condition. \(500/60\) or \(8.\overline{3}\) represents the number of multiples of 60. Of course, multiples can only be counted as whole numbers, so there are only 8 integers that are divisible by 3,4, and 5.