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ab=mcm{a,b}·mcd{a,b}
(mcd{a,b}·p)·(mcd{a,b}·q)=mcm{a,b}·mcd{a,b}


mcm{a,b+c}·mcd{a,b+c}=mcm{a,b}·mcd{a,b}+mcm{a,c}·mcd{a,c}


mcm{a,a+b}·mcd{a,a+b}=a^{2}+mcm{a,b}·mcd{a,b}
mcm{a,a+b}=(a^{2}/mcd{a,b})+mcm{a,b}


mcm{3,6}=mcm{3,3+3}=(9/3)+3=3+3=6
mcm{3,7}=mcm{3,3+4}=9+12=21
mcm{3,8}=mcm{3,3+5}=9+15=24
mcm{3,9}=mcm{3,3+6}=(9/3)+6=3+6=9


mcm{5,10}=mcm{5,5+5}=(25/5)+5=5+5=10
mcm{10,15}=mcm{10,10+5}=(100/5)+10=20+10=30
mcm{2k,2k+1}=4k^{2}+2k=2k(2k+1)
mcm{2k,3k}=mcm{2k,2k+k}=(4k^{2}/k)+2k=4k+2k=6k
mcm{nk,(n+1)k}=mcm{nk,nk+k}=(n^{2}k^{2}/k)+nk=n^{2}k+nk=(n^{2}+n)k=n(n+1)k


(na)·(nb)=mcm{na,nb}·mcd{na,nb}
n^{2}·(ab)=mcm{na,nb}·mcd{na,nb}
n^{2}·mcm{a,b}·mcd{a,b}=mcm{na,nb}·(n·mcd{a,b})
n·mcm{a,b}=mcm{na,nb}


mcm{3,12}=mcm{3,3·4}=3·mcm{1,4}=3·4=12


n=mcm{n,1}·mcd{n,1}
n=mcm{n,1}


mcm{a,a+1}=a^{2}+a=a(a+1)