GCD & LCM

For any two positive integers $a$ and $b$, the product of their highest common factor and lowest common multiple equals the product of the numbers: $\text{H.C.F.}(a,b)\times \text{L.C.M.}(a,b)=ab$. To find the H.C.F. or L.C.M. of fractions, apply the operation to the numerators and denominators separately: $\text{H.C.F.}\left(\frac{a}{b},\frac{c}{d}\right)=\frac{\text{H.C.F.}(a,c)}{\text{L.C.M.}(b,d)}$ and $\text{L.C.M.}\left(\frac{a}{b},\frac{c}{d}\right)=\frac{\text{L.C.M.}(a,c)}{\text{H.C.F.}(b,d)}$. For several integers, find the H.C.F. by taking the lowest power of each common prime factor, and the L.C.M. by taking the highest power of every prime factor appearing.