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