Determine the LCM and GCD for the following and prove that \(f(x) \times g(x) = LCM \times GCD\).
\(26 x^2 y\), \(247 xy^2\)
Answer:
Let \(f(x) = 26 x^2 y\) and \(g(x) = 247 xy^2\)
\(LCM(26x^2 y, 247xy^2) =\)
\(GCD(26x^2 y, 247xy^2) =\)
Now, we shall prove that \(f(x) \times g(x) = LCM \times GCD\).
\(f(x) \times g(x)\) \(=\) ---- (\(1\))
\(LCM \times GCD\) \(=\) ---- (\(2\))
From equations (\(1\)) and (\(2\)), we see that LHS \(=\) RHS.
Therefore, \(f(x) \times g(x) = LCM \times GCD\).
Hence, proved.