Don't ask me how it works (I have not yet examined it enough to know).
Originally Posted by Pinky&The Brain
ANyway, the method is this:
pick any amount of numbers, let's do 18; 32; and 3
Now to find the LCM of all of them we write out there prime factors:
now this will sound confusing...
Number Prime Factors
18 2^1 x 3^2
32 2^5 x 3^0
3 2^0 x 3^1
take a look at those prime factorizations, the only prime factors for those three numbers are 2's and 3's. Therefore our LCM has prime factors of 2's and 3's
LCM = 2^a x 3^b
now (here's the part that get's everybody), find the biggest group for each prime factor, In this case the biggest group for 2 is 2^5, and the biggest group for 3 is 3^2. Now put that into your equation to get:
LCM = 2^5 x 3^2 = 32 x 9 = 288
so the lowest common multiple for 18, 32, and 3 is 288
Now you try to find the LCM of 3; 4; and 10; and I'll correct your work.