If the LCM of two integers P, Q (where Q> P and P>1) is P*Q, then which of the following can not be true? Answers:
A) Both P and Q can be consecutive integers.  B) Both P and Q can be Prime Numbers.  C) P and Q do not have a common factor.  D) P and Q do not share any Prime factors.  E) All Prime factors of P must be Prime factors of Q.
If LCM of two numbers P and Q is the product PQ 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, B, C and D are all true.   Only Option E cannot be true.   Hence answer is All Prime factors of P must be Prime factors of Q.
<result>E</result>
If the LCM of two integers P, Q (where Q> P and P>1) is P*Q, then which of the following can not be true?