Richie says the least common multiple of a pair of prime numbers is the product of the 2 numbers. Is he right or wrong? Explain your reasoning.

hi Ms. Sue

A product is the answer to a multiplication problem.

Richie is wrong. The least common multiple (LCM) of any pair of prime numbers is equal to the product of the two numbers only if the two prime numbers are distinct.

To explain this, let's first define what a least common multiple (LCM) is. The LCM of two or more numbers is the smallest number that is divisible by each of the given numbers without leaving a remainder.

Now, let's consider a scenario where the two prime numbers are different, such as 3 and 5. The LCM of 3 and 5 is indeed the product of the two numbers, which is 15.

However, if the two prime numbers are the same, such as 7 and 7, then the LCM is not simply the product of the two numbers. In this case, the LCM is equal to the number itself, which is 7.

Hence, we can conclude that Richie's statement is incorrect as it does not hold true for all pairs of prime numbers.

A product

prime numbers could be 2, 3, 5, 7, 11, etc.

What happens with 2, 3 which gives us 6?

or with 5, 7 which gives us 35?

Can you finish it from here?

I don't understand the product of the two numbers