SOLUTION: The positive integer N has exactly eight different positive integral factors. Two of these factors are 15 and 21. What is the value of N?

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Note that 15 = 3*5 and 21 = 3*7. The LCM of 15 and 21 is 3*5*7 = 105, however this already has eight factors (use the algorithm for finding the # of factors of a number, add 1 to each exponent, multiply). Therefore N = 105.