How can you determine whether the LCM of two numbers is the product of the numbers or is less than the product of the numbers

Question

 

 It doesn't make sense how its telling you the product of the numbers or less.

Answer 1

If the two numbers have a common factor, it is included twice in their product.  Divide the product by the largest common factor to get the LCM.

 

4 x 6 = 24

each has 2 as a factor.

24 / 2 = 12 = LCM

 

Here's how I find the LCM when I can't just do it in my head:

18 and 27

Find the factors of each:

18 = 3 * 3 * 2

27 = 3 * 3 * 3

 

Start with the factors of one of the numbers:

3 * 3 * 2

What new factors do you need to add for the next number:

27 needs three 3's. We already have two 3's in our list, so we just need to add one more.

3 * 3 * 2 * 3 = 54 is the LCM.

This includes all of the factors of either number, so it's divisible by both.

We didn't include a bunch of extra 3's that would have been in the product of 18 and 27.

 

You can keep going if you have more than two numbers that you need the LCM for.  You just add new factors as you find expanded requirements for each new number.  For example, if our original list of numbers had a 6 in it, it would not change the LCM.  Our list for 54 already has a 2 and a 3 in it.

 

Answer 2

If one of the numbers is a multiple of the other, their lcm is less than the product of the numbers.

 

For example, with 10 and 5, their lcm is 10 but their product is 50.