If the L.C.M of two numbers such that L.C.M (26, 91) = 182, then find the H.C.F of (26, 91).

If the LCM of two numbers is 182 and those numbers are 26 and 91, we can use the relationship between LCM and HCF (Highest Common Factor) for two numbers to find the HCF.  
LCM × HCF = Product of two numbers
The L.C.M of 26 and 91 is 182. So,
$\mathrm{H}.\mathrm{C}.\mathrm{F} =\frac{ \mathrm{product} \mathrm{of} \mathrm{two} \mathrm{numbers} }{\mathrm{L}\cdot \mathrm{C}\cdot \mathrm{M}}$
$\mathrm{H}.\mathrm{C}.\mathrm{F }=\frac{\mathrm{ }91\times 26}{182}$

$\mathbf{H}\mathbf{.}\mathbf{C}\mathbf{.}\mathbf{F}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{13}$
Therefore, the HCF of 26 and 91 is 13.