The set of all positive integers that are divisible by both 15 and 35 is infinite. What is the least positive integer in this set?

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Write the first few multiples of each number until you see a number in common:

$$ 15, 30, 45, 60, 75, 90, 105... $$ $$ 35, 70, 105... $$

The factors of each number are:

$$ 15 = 5\cdot 3 $$ $$ 35 = 5\cdot 7 $$

Therefore the least common multiple would be:

$$ 5\cdot 3\cdot 7 = \boxed{105} $$