Question

Find LCM and HCF of the following integers by using prime factorization method: 42, 63 and 140

Answer 1

AnswEr :

$\bf{\underline{\underline{\bf{Given\::}}}}}}$

We have integers by using prime factorization method : 42, 63 & 140.

$\bf{\underline{\underline{\bf{To\:find\::}}}}}}$

The L.C.M and H.C.F.

$\bf{\underline{\underline{\bf{Explanation\::}}}}}}$

$\mathcal{\underline{\red{L.C.M\:(LOWEST\:COMMON\:MULTIPLE)\::}}}$

$\begin{array}{r|l} 2 & 42,63, 140\\ \cline{2-2} 2 & 21,63,70\\ \cline{2-2} 3& 21,63,35\\ \cline{2-2} 3& 7,21,35\\ \cline{2-2} 5& 7,7,35\\ \cline{2-2} 7& 7,7,7\\ \cline{2-2} & 1,1,1\end{array}$

L.C.M. = 2 × 2 × 3 × 3 × 5 × 7 = 1260.

&

$\mathcal{\underline{\red{H.C.F\:(HIGHEST\:COMMON\:FACTOR)\::}}}$

$\star$ H.C.F. of 42 :

$\begin{array}{r|l} 2 & 42\\ \cline{2-2} 3 & 21\\ \cline{2-2} 7&7\\ \cline{2-2} &1 \end{array}$

$\star$ H.C.F. of 63 :

$\begin{array}{r|l} 3 & 63\\ \cline{2-2} 3 & 21\\ \cline{2-2} 7&7\\ \cline{2-2} &1 \end{array}$

$\star$ H.C.F. of 140 :

$\begin{array}{r|l} 2& 140\\ \cline{2-2} 2 & 70\\ \cline{2-2} 5&35\\ \cline{2-2}7 &7\\ \cline{2-2} & 1 \end{array}$

$\bf{42=\sf{2\times 3\times \boxed {7}}}\\\\\bf{63=\sf{3\times 3\times \boxed {7}}}\\\\\bf{140=\sf{2\times 2\times 5\times \boxed {7}}}$

$\therefore\red{\small{\underline{\sf{The\:H.C.F.(42,63,140)=7}}}}$

Answer 2

$\large \underline{ \blue{ \boxed{ \bf \green{Required \: Answer}}}}$