I hate these problems with a passion. I've been told to do these 800 ways but nothing seems to work everytime. Take this problem for example:
The LCM of 36, 24, and 20 is... _________________
So... Lets say you take the GCD of these 3 numbers, which is 4, and divide into each of the numbers respectably: you get 9, 6, and 5. Now multiply 4 by all these numbers, and you should have the LCM, right? WRONG! 9 * 6 * 5 * 4 = 1080. That is obviously incorrect. Anyone that has worked with circular angles before is gonna say that 360 is your answer, and of course, thats right. I just want to know how to do these. Help?
take the LCM of two numbers, the ones that are usually multiples of the same number(36 and 24). You should be able to get 72 quickly. Take 72 and the third number and find the GCD.
72,20 LCM = 360 which can be obtained by looking at it for a second or
(you probably know this method) LCM of 2 numbers = a*b / GCD
Dern... That seems like alot of work for just one problem. I'm thinking that your way is probably fastest, but I hate finding the freaking LCM!!! To me, 2 numbers is difficult as far as LCM is concerned. This is what I've tried:
First, start out by taking the gcf like I tried earlier, and divide it out. Next, look for any common divisors left between any 2 of the three numbers and divide it out as well.
36 = 2*2*3*3
24 = 2*2*2*3
20 = 2*2*5
GCF = 4. Divide out, and remember it. You're now left with 9,6, and 5. divide out the three and remember it. So now you have 2*3*3*4*5, and that equals 360. This still isn't fast or reliable. Any other ways?
It's not that much work ... the first LCM between the two multiples of the same number should be quick and pretty much all LCM of 3 numbers have two multiples of the same number.
Vinay ('sup, man!) and Brad's factoring will work --- PROVIDED THAT I CAN REMEMBER ALL THOSE DARN PRIMES AND INDICES IN MY HEAD!
My way is kind of hard to articulate, to put it simply: just look at it, and think about it.
It is quite risky,though. Because for 36.24.20, I would say something like 720 within 5 seconds, but it takes a bit longer to realize that 360 works better. However, by that time I must have already written down 720, so BAH UGH PBHT, what the heck, and I'll just move on.
I have seen a nastier form of questions. One example would be:
What is the sum of all the proper but unreducible fractions of 24 ______ (mixed number).
I think an easier version has appeared in Skow's tests. White and Dr. Numsen have never had any of these. But this is something nice to know. Because Mr. White can put it in MA or even NS tests this year. In fact, he can do anything!
This is quite a hard NS question. And a shortcut would be nice.
