Question 825146
LCM, Lowest Common Multiple.


Just make several of the first whole number multiples of each number and look for the first multiple or product which occurs for both of the given numbers.


___________14______________32
2__________28______________64
3__________42______________96
4__________56______________128
5__________70______________160
6__________84______________192
7__________98______________224
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Still not done...

Want better way?

Factor each given starter number into its prime factorization.
{{{14=2*7}}};
{{{32=4*8=2^2*2^3=2^5}}}.


The LCM you want is the number which has the highest count of each of the involved prime factors of each given number.  The 7 occurs 1 time; the 2 occurs 5 times.  The lowest common multiple for 14 and 32 is {{{highlight(7*2^5=highlight(224))}}}.


Obviously found was {{{7*32=224}}}, but you can examine this factorization to see how 14 is used as one of the factors to get 224 as product:  {{{14*2^4=14*16=224}}};  you see already how one-by-one separate multiplications can consume so much time.