Question

Find the HCF 456 and 360 by prime factorisation method. Hence find their LCM?

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}456\mathrm{and}360\mathrm{is}\mathrm{given}\mathrm{by} \\ 456=2\times 2\times 2\times 3\times 19 \\ 360=2\times 2\times 2\times 3\times 3\times 5 \\ \mathrm{HCF}=2\times 2\times 2\times 3=24 \\ \mathrm{Now}, \\ \mathrm{HCF}\times \mathrm{LCM}=\mathrm{product}\mathrm{of}2\mathrm{numbers} \\ \Rightarrow \mathrm{LCM}=\frac{\mathrm{product}\mathrm{of}2\mathrm{numbers}}{\mathrm{HCF}} \\ \Rightarrow \mathrm{LCM}=\frac{456\times 360}{24}=6840 \end{gathered}$$