The School of Fine Art has 100 lockers numbered 1 through 100. At present, all lockers are open. We begin by closing every locker whose number evenly divides by 3. Then we toggle each locker whose number is divisible by 4. (Toggling means opening a closed locker and closing an open locker.) Next, we toggle each locker whose number is divisible by 5. We count upward and continue this with each number, until finally, we toggle each locker whose number is divisible by 100. How many lockers are now open?