If the LCM of two integers X, Y (where Y> X and X>1) is X*Y, then which of the following can not be true?	Choose one
A) Both X and Y can be Prime Numbers.  B) All Prime factors of X must be Prime factors of Y.  C) Both X and Y can be consecutive integers.  D) X and Y do not share any Prime factors.  E) X and Y do not have a common factor
If LCM of two numbers X and Y is the product XY then both numbers are Co- prime.   (Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).   Numbers that can be Co-Prime are :   1) Two consecutive natural numbers.   2) Two consecutive odd numbers.   3) Two prime numbers.   4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.   With above four statements it can be concluded that Options A, C, D and E are all true.   Only Option B cannot be true.   Hence answer is All Prime factors of X must be Prime factors of Y.
<result>B</result>
If the LCM of two integers X, Y (where Y> X and X>1) is X*Y, then which of the following can not be true?