How do you figure out the lowest common multiple?

in school we are learning the LCM and i get what to do, however i want to try the way by x a common number and from there. for instance;


the lcm of 21 and 12 would be worked out like this:


12= 2 x 2 x3


21= 3 x 7.


why has 3 been used ?


thanks.How do you figure out the lowest common multiple?
because if it was two then it'd be 12=2x6 but the 6 can be broken down even further. that's why it's turned into 12=2x2x3


however neither 3 nor 7 can be broken down so it's just left like that.


hope i helped :)How do you figure out the lowest common multiple?
to find the LCM, factor both numbers:





12 = 2*2*3


21 = 3*7





take the highest number used of each factor. Two twos, one seven, one three (not two threes, only one three - that's the highest number of threes present in any single number present)





so we have 2*2*3*7 = 84