LUANDATO wrote:If N is a positive integer and 14N/60 is an integer. What is the smallest value of N for which N has exactly four different prime factors?
A)30
B)60
C)180
D)210
E)cannot be determined
14N/60 = 7N/30.
The smallest prime numbers are 2, 3, 5 and 7.
Thus, the smallest integer with 4 different prime factors = 2*3*5*7 = 210.
Test whether N=210 yields an integer value for 7N/30:
(7*210)/30= 7*7 = 49.
Success!
Thus, the least possible value for N = 210.
The correct answer is
D.
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