Ms Math's kindergarten class has 16 registered students. The classroom has a very large number, N, of play blocks which satisfies the conditions:
(a) If 16, 15, or 14 students are present in the class, then in each case all the blocks can be distributed in equal numbers to each student, and
(b) There are three integers 0 < x < y < z < 14 such that when x, y, or z students are present and the blocks are distributed in equal numbers to each student, there are exactly three blocks left over.
Find the sum of the distinct prime divisors of the least possible value of N satisfying the above conditions.
A right angled triangle is such that its hypotenuse is equal to 65 centimeters (cm) and its inradius is equal to 12 cm. The length of the other two sides, when expressed in cm, are positive integers.
Determine the perimeter of the triangle.
NOTE: The inradius is defined as the radius of the inscribed circle.
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