2.Find HCF and LCM of 426 and 576 by prime factorisation method and verify that LCM X HCF = product of the numbers.
Answers
Answer:
hello mate..
Step-by-step explanation:
Answer:
\begin{tabular}{l|r}2&426\\\cline{1-2}3&213\\\cline{1-2}&71\end{tabular}\qquad\qquad\begin{tabular}{l|r}2&576\\\cline{1-2}2&288\\\cline{1-2}2&144\\\cline{1-2}2&72\\\cline{1-2}2&36\\\cline{1-2}2&18\\\cline{1-2}3&9\\\cline{1-2}&3\end{tabular}\\\\\bigstar\:\underline{\tt Prime\: Factorization:}\\\\\bf{\dag}\:\sf 426=2\times3\times71\\\\\bf{\dag}\:\sf576=2\times2\times2\times2\times2\times2\times3\times3
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☯ HCF of (426, 576) :
:\implies\sf HCF = Highest\: Common\: Factor\\\\\\:\implies\sf HCF=2 \times 3\\\\\\:\implies\textsf{HCF (426, 576) = 6}
\rule{100}{0.8}
☯ LCM of (426, 576) :
:\implies\sf LCM=Least\: Common\: Multiple\\\\\\:\implies\sf LCM=2^6 \times 3^2 \times 71\\\\\\:\implies\sf LCM=64 \times 9 \times 71\\\\\\:\implies\textsf{LCM (426, 576) = 40,896}
\rule{190}{2}
⠀⠀⠀⠀⠀⠀⠀⠀Verification
\dashrightarrow\sf\:\: Product\:of\: Numbers=HCF\times LCM\\\\\\\dashrightarrow\sf\:\:426 \times 576=6 \times 40896\\\\\\\dashrightarrow\textsf{\:\:245,376 = 245,376} \\\\{\qquad \underline{\mathcal{HENCE\: \:VERIFIED}}}