Two positive integers m and n are chosen such that m is the largest positive integer less than 100 with only two positive divisors and n is the smallest integer with exactly three positive divisors. What is m + n?
Two positive integers m and n are chosen such that m is the largest positive integer less than 100 with only two positive divisors and n is the smallest integer with exactly three positive divisors. What is m + n?
If the number is to have only two divisors,
then at least one of the divisors has to be prime.
So how about taking the largest prime less than 50,
and doubling it, so that would be 47 x 2, thus m = 94
If 1 is qualified to be considered a divisor, then m = 97 but I don't like that.
The other number, smallest with three divisors, I just used the
three smallest factors, so, that would be 2 x 3 x 5, thus n = 30
Final answer, m + n = 124
If you wanted to qualify 1 as a divisor, you can find n the same way.
