បង្ហាញថា
( m , n ) [ m , n ] = m n {\displaystyle (m,n)[m,n]=mn}
តាង p {\displaystyle p} ជាចំនួនបឋមដែល
p e = m {\displaystyle p^{e}=m}
p f = n {\displaystyle p^{f}=n}
ប្រសិនបើ e ≤ f {\displaystyle e\leq f}
នោះ
( m , n ) = p e {\displaystyle (m,n)=p^{e}}
[ m , n ] = p f {\displaystyle [m,n]=p^{f}}
( m , n ) [ m , n ] = p e + f {\displaystyle (m,n)[m,n]=p^{e+f}}
តែ
m n = p e + f {\displaystyle mn=p^{e+f}}
មានន័យថា
( l , m , n ) [ l m , m n , n l ] = l m n {\displaystyle (l,m,n)[lm,mn,nl]=lmn} ចំពោះចំនួនគត់រ៉ឺឡាទីបវិជ្ជមាន l , m , {\displaystyle l,m,} និង n {\displaystyle n} ។
p d = l {\displaystyle p^{d}=l}
បើ
d ≤ e ≤ f {\displaystyle d\leq e\leq f}
d + e ≤ d + f ≤ e + f {\displaystyle d+e\leq d+f\leq e+f}
( l , m , n ) = p d {\displaystyle (l,m,n)=p^{d}}
[ l m , m n , n l ] = p e + f {\displaystyle [lm,mn,nl]=p^{e+f}}
គេបាន
( l , m , n ) [ l m , m n , n l ] = p d + e + f {\displaystyle (l,m,n)[lm,mn,nl]=p^{d+e+f}}
l m n = p d + e + f {\displaystyle lmn=p^{d+e+f}}
( l , m , n ) [ l m , m n , n l ] = l m n {\displaystyle (l,m,n)[lm,mn,nl]=lmn}
![{\displaystyle (m,n)[m,n]=mn}](https://wikimedia.org/api/rest_v1/media/math/render/svg/53d5837e4b79355627242cfe72e6576a1b427d30)
ជាចំនួនបឋមដែល
![{\displaystyle [m,n]=p^{f}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8c9df9c4641229d5dc148ea1e4b0b45605200208)
![{\displaystyle (m,n)[m,n]=p^{e+f}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84c6dff11fd1f57d13d36c4b96c28103f39e46ee)
![{\displaystyle (l,m,n)[lm,mn,nl]=lmn}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97e2e13c77b2641218cead17aec21f36adde0233)
ចំពោះចំនួនគត់រ៉ឺឡាទីបវិជ្ជមាន 
និង 
។
ជាចំនួនបឋមដែល
![{\displaystyle [lm,mn,nl]=p^{e+f}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a19d3249e18c7f3039f5459ccad2c2d28a9dd311)
![{\displaystyle (l,m,n)[lm,mn,nl]=p^{d+e+f}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2b96c415876e89ff50302b43bd4d1a72a2591c59)
