Question

​​1. Find the LCM of 315 and 360 by the prime factorization method. Hence, find their HCF.
2. Find the HCF of 300, 360 and 120 by the prime factorization method.
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Answer 1

$$\begin{gathered} \left(1\right). \\ \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}315\mathrm{and}360\mathrm{is} \\ 315=3\times 3\times 5\times 7 \\ 360=2\times 2\times 2\times 3\times 3\times 5 \\ \mathrm{LCM}\mathrm{of}315\mathrm{and}360=2\times 2\times 2\times 3\times 3\times 5\times 7=2520 \\ \mathrm{Now},\mathrm{HCF}=\frac{\mathrm{Product}\mathrm{of}315\mathrm{and}360}{\mathrm{LCM}}=\frac{315\times 360}{2520}=45 \\ \left(2\right). \\ \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}300,360\mathrm{and}120: \\ 300=2\times 2\times 3\times 5\times 5 \\ 360=2\times 2\times 2\times 3\times 3\times 5 \\ 120=2\times 2\times 2\times 3\times 5 \\ \mathrm{HCF}=2\times 2\times 3\times 5=60 \end{gathered}$$