Kritisood
Find the lowest number which has both X and Y as factors, where X and Y are positive integers.
(1) X and Y have no common prime factors and X^2 Y^2 = 169*4
(2) 2Y = 13X and lowest prime factor of X is X
This is the same as asking for the least common multiple of X and Y.
Statement 1:Since they have no common prime factors, their greatest common factor (GCF) is 1 and their LCM must be \(X*Y.\) We know the value of \(X*Y = 13 * 2\) so this is sufficient.
Statement 2:The lowest prime factor of X is X, then X must be prime. Next, we have \(X = \frac{2Y}{13}\). First of Y must be a multiple of 13 in order to have X as an integer. In order to have X as a prime number, the value of Y must be 13. If Y was any other multiple of 13, X would have an extra factor. Now since we know the value of both X and Y, this is sufficient.
Ans: D
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