Answer:
The statement "The LCM of two numbers is the product of the two numbers" is sometimes true, but not always.
Explanation:
Here are two examples to support this reasoning:
Example 1:
Consider the two numbers 6 and 10.
The factors of 6 are 1, 2, 3, and 6.
The factors of 10 are 1, 2, 5, and 10.
The common factors are 1 and 2, so the GCF of 6 and 10 is 2.
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
The smallest multiple that is common to both lists is 30, so the LCM of 6 and 10 is 30.
However, the product of 6 and 10 is 60, which is not equal to the LCM of 6 and 10.
Therefore, in this case, the statement "The LCM of two numbers is the product of the two numbers" is false.
Example 2:
Consider the two numbers 5 and 7.
The factors of 5 are 1 and 5.
The factors of 7 are 1 and 7.
The GCF of 5 and 7 is 1.
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ...
The smallest multiple that is common to both lists is 35, so the LCM of 5 and 7 is 35.
The product of 5 and 7 is 35, which is equal to the LCM of 5 and 7.
Therefore, in this case, the statement "The LCM of two numbers is the product of the two numbers" is true.
So, we can see that the statement is sometimes true, depending on the specific numbers being considered.