Please help with math problem!!!

[mrsgus06]

My oldest dd has a math problem that is kicking our rears!

The LCM (lowest common multiple?) of two numbers is 120. The GCF (greatest common factor?) is 6. One number is 6 more than the other. What are the numbers?

We can not figure this one out!! Please help and explain how you got the answer. Thanks in advance.

 

[Madaboutthemouse]

Try 24 and 30.
Multiples of 24: 24, 48, 72, 96, 120
Multiples of 30: 30, 60, 90, 120
So, LCM would be 120
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
So, GCF would be 6

I found the answer by checking the factors of 120
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. There are only a few that are 6 apart...6 and 12, 24 and 30. 6 and 12 didn't fit the LCM rule, their LCM would be 12. Hope this helps!

 

[salmoneous]

Note sure if this is the textbook way to do it, but factor 120 to get 2x2x2x3x5. If we factor the two numbers we are looking for, they can only use numbers from that group. We also know they both use (at least) one 2 and the 3. A quick guess would be

First number 2x3x2x2 = 24
Second number 2x3x5 = 30

Checking the work, you can see that these numbers have an LCM of 120, a GCF of 6, and are 6 appart.

 

[damo]

Since the LCM is 120, start by writing out all the factors of 120: 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Choose two of these factors that have a difference of 6 (that would be 24 and 30). Check that the LCM is 120. It is.

Check to see that the GCF is 6. It is since the factors of 24 are 1,2,3,4,6,8,12,24 and the factors of 30 are 1,2,3,5,6,15,30. So the GCF is indeed 6.

Therefore, your two numbers are 24 and 30

 

[Mi3stooges]

My DD struggles in Math and I haven't a clue (Been there done that!!LOL) But we use this website and it really helps

www.math.com

 

[mrsgus06]

Thank you all! I had all the factors for 120, but I think our mistake was trying to multiply them together to get 120. Had all the right numbers, but a "brain fart" occured. Maybe it was because it was Pizza night at CC's Pizza for the school and there were too many kids running around to concentrate! Oh, wait, my kids were the only ones there! Oh well, thank you again!