When one of the numbers is prime and the other is 1.
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None of them can.
A semiprime or a prime square.
679 is the product of the largest single-digit prime number and the largest two-digit prime number.
a composite number seems a reasonable answer.
If the second number is a multiple of the prime number, than the LCM is the second number. If the second number is not a multiple of the prime number, then the two numbers are relatively prime, and the LCM is the product of the two numbers.