If HCF of two numbers is 6 and lcm of two same two numbers is 72.Find the numbere
Since their HCF is 6, let the numbers be 6m and 6n
Now apply the formula. (Also note that m and n are coprime, i.e. gcd(m,n)=1
You'll get :6m×6n=6×72⟹mn=12 ; m,n∈N
Now the possible unordered pairs of (m,n)are :(1,12);(2,6);(3,4)
Out of which only the pair (3,4) is coprime.
Hence, the numbers are : 18 and 24