Question

Find HCF and LCM of 426 and 576 by prime factorization method and verify that LCM X HCF = product of the numbers

Answer 1

2l426

3l213

71

★ Prime factor of 426 = 2 × 3 × 71

2l576

2l288

2l144

2l72

2l36

2l18

3l9

3

★ Prime factor of 576 = 2⁶ × 3²

Hence,

H.C.F ( 426,576 ) = 2 × 3 = 6

L.C.M ( 426,576 ) = 2⁶ × 3² × 71 = 64 × 9 × 71 = 40,896

Verify:

L.C.M × H.C.F = Product of two numbers

⇒ 6 × 40,896 = 426 × 576

⇒ 245,376 = 245,376

Therefore, L.HS = R.HS

verified.

Answer 2

Answer:

$\begin{tabular}{l|r}2&426\\\cline{1-2}3&213\\\cline{1-2}&71\end{tabular}\qquad\qquad\begin{tabular}{l|r}2&576\\\cline{1-2}2&288\\\cline{1-2}2&144\\\cline{1-2}2&72\\\cline{1-2}2&36\\\cline{1-2}2&18\\\cline{1-2}3&9\\\cline{1-2}&3\end{tabular}\\\\\bigstar\:\underline{\tt Prime\: Factorization:}\\\\\bf{\dag}\:\sf 426=2\times3\times71\\\\\bf{\dag}\:\sf576=2\times2\times2\times2\times2\times2\times3\times3$

⠀

☯ 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

$\dashrightarrow\sf\:\: Product\:of\: Numbers=HCF\times LCM\\\\\\\dashrightarrow\sf\:\:426 \times 576=6 \times 40896\\\\\\\dashrightarrow\textsf{\:\:245,376 = 245,376} \\\\{\qquad \underline{\mathcal{HENCE\: \:VERIFIED}}}$