### Challenge: Shortcut to find LCM...

Jennifer thinks there is a shortcut to find out lowest common multiple (LCM) of 2 numbers.

She says that,
"If you multiple the two numbers, you will ALWAYS get the LCM."
Is Jennifer right?

Does her method work every time? Sometimes? Never?

Explain your reasoning.
Illustrate your reasoning with examples.

Source: http://ims.ode.state.oh.us/

#### 12 comments:

1. Jennifer's method is a way of getting the common multiple of to numbers, but still her method is still workable, it can get the LCM sometimes on particular numbers.

2. Her method only works sometimes. If she is finding the lowest common multiple of 2 and 3 for example, it will work. However if she she was finding the lowest common multiple of 4 and 16 for example, hermethod would not work.

3. I think her method only works sometimes as it depends on the numbers being used for this method to work.

4. Her method does not always work. For example if the numbers 3 and 6 it does not work but the numbers are 2 and 3 it works in conclusion it only works for some numbers.

5. Her method doesn't always work.

6. Her method doesn't always work.
For Example: If she multiplies 6,5,4, she gets 120 however the lowest common multiple of 6,5 and 4 is 60.

7. Her method does not always work.

For example. The LCM of 4 & 2 is 4, however 4 X 2 is 8

8. Her method will not work all the time. Take these examples: Find the LCM of 10 and 20. If we use her method it would turn out as 200 but really the LCM is 20. Another example: Find the LCM of 5 and 6,in this you can use her method the answer is 30

9. Jennifer method does not always work as the LCM can be something lower than the numbers multiplied by each other. This method usually works for the smaller pairs of numbers with one or all odd numbers. Also, if a prime number is included, then her method works, so in other words, Jennifer's statement is incorrect.

10. Jennifer method works sometimes like if the two numbers are 9 and 7, but if the numbers are 100 and 200, it would not,

11. Her method is wrong as we would not get the LCM always by that method.

Her method would not work every time. For example, the LCM of 6&9 is 18 and not 54 which you get by multiplying both of the numbers but sometimes it works for examples such as 7&9. Their LCM is 63 which is the value you get if you multiply both of them together.

12. It works, but not always.

eg. The LCM of 6 and 4

6x4=24

However the LCM of 6 and 4 is 12