Math help needed. Least common multiple and prime factors

[iLovDisney]

DS needs to find the LCM of numbers like 24 and 30. The instructions say to use prime factorization. We can find the prime factors but don't know how to use them to get the Least Common Multiple.

Help!

 

[Kermit]

I *think* that the least common multiple is the list of numbers that you can multiply together to get that number. They should all be prime numbers. For example, 24 would be 3 X 2 X 2 X 2.

 

[iLovDisney]

The Least Common Multiple is the smallest number that is a multiple of 2 certain numbers.

The LCM of 2 and 5 is 10. It's when the numbers get larger that things get tricky.

The LCM of 24 and 30 is ???

I know that 240 is a common multiple, but I don't know if it's the smallest one. And I don't know how prime factors come into it.

ick

 

[BobBrazeal]

I do believe that 240 is the correct answer. The process to get there is in several steps.

1. Find the prime factors of both numbers.

24 - 3 x 2 x 2 x 2
30 - 5 x 3 x 2

2. From the prime factors, find the Greatest Common Factor (the largest number(s) that appears in both lists.

In this case - 3 & 2 so the Greatest Common Factor is 6

3. Multiply the two original numbers together and divide by the Greatest Common Factor to get the Least Common Multiple.

24X30/6= 120

(Corrected after Talking Hands (Lisa) pointed out my error. Thank you)

 

[iLovDisney]

GROOVY!!

Thank you so much Bob.

 

[nativetxn]

Bob, you are amazing

 

[Talking Hands]

Actually the LCM is 120 not 240.

 

[BobBrazeal]

You're exactly right! Been way too long for my basic math.

Of course, if I had taken a few moments to look at the prime factors rather than jumping in with a reply I would have caught that the Greatest Common Factor is 3 x 2 not just 3! Duh!!

Thanks, Talking Hands. That's what I get for answering questions too quickly.

I do believe that the process is correct, just that I made a mistake at step two when going through the steps. -- Now edited above.

 

[browneyes]

Math! ACK!

 

[Buckalew]

Ack! Is the common basic math?? Boy, I'm in trouble!

LYNNE!!!!!!

 

[Pin Wizard]

AAAAAAuuuuggghh! I just closed my algebra book not too long ago. I really hope this tree stuff isn't on my final tomorrow because it makes no sense whatsoever to me.