Given m=24⋅32⋅11m = 2^4 \cdot 3^2 \cdot 11m=24⋅32⋅11 and n=22⋅33⋅5n = 2^2 \cdot 3^3 \cdot 5n=22⋅33⋅5, which of the following are CORRECT?
gcd(m,n)=22⋅32\gcd(m,n) = 2^2 \cdot 3^2gcd(m,n)=22⋅32
lcm(m,n)=24⋅33⋅5⋅11\text{lcm}(m,n) = 2^4 \cdot 3^3 \cdot 5 \cdot 11lcm(m,n)=24⋅33⋅5⋅11
gcd(m,n)⋅lcm(m,n)=m⋅n\gcd(m,n) \cdot \text{lcm}(m,n) = m \cdot ngcd(m,n)⋅lcm(m,n)=m⋅n
The prime 5 divides gcd(m,n)\gcd(m,n)gcd(m,n)