Question

Find the H.C.F of $180$and $336$. Also , find their L.C.M.

Answer 1

Step 1 : Find the H.C.F. ( Highest Common Factor ) by prime factorization

Prime factors of :

$$\begin{gathered} 180=2\times 2\times 3\times 3\times 5 \\ 336=2\times 2\times 2\times 2\times 3\times 7 \end{gathered}$$

Notice that $2$ occurs as a common prime factor for two times and $3$ for at least once in both the given numbers. Highest Common Factor ( H.C.F. ) $$\begin{gathered} =2\times 2\times 3 \\ =12 \end{gathered}$$

H.C.F $=12$

Step 2 :Find the L.C.M.( Lest common multiple )

$\mathrm{L}.\mathrm{C}.\mathrm{M}.=\frac{\mathrm{Product}\mathrm{of}\mathrm{two}\mathrm{numbers}}{\mathrm{their}\mathrm{HCF}}$

$$\begin{gathered} =\frac{180\times 336}{12} \\ =\frac{15\times 336}{1}\left[\mathrm{Cancel}180\mathrm{and}12\mathrm{by}12\right] \\ =5040 \end{gathered}$$.

Hence , H.C.F. of $180$ , $336$ is $12$ and L.C.M of $180,336$ is $5040$