Question

मूळ अवयव पाडून मसावि व लसावि काढा: 32, 24, 48

Answer 1

उत्तर :

लसावि = 96

मसावि = 8

ल.सा.वि.( लघुत्तम साधारण विभाजक) दिलेल्या संख्यानी ज्या लहांनात लहान संख्येला पूर्ण भाग जातो ती संख्या म्हणजे त्यांचा ल.सा.वि. होय.

लसावि : 32, 24, 48

$\begin{array}{r|l}2 & 32,48,24 \\\cline{1-2} 2 & 16,24,12 \\\cline{1-2} 2 & 8,12,6\\ \cline{1-2} 2 & 4,6,3\\\cline{1-2} 2& 2,3,3\\\cline{1-2}3&1,3,3\\\cline{1-2}&1,1,1\end{array}$

लसावी = 2 × 2 × 2 × 2 × 2 × 3

$\tt{\implies2 \times 2 \times 2 \times 2 \times 2 \times 3}$

$\tt{\implies4 \times 4 \times 6}$

$\tt{\implies16 \times 4}$

$\tt{\implies96}$

$\therefore$ लसावि = 96

म.सा. वि. (महत्तम साधारण विभाजक) दिलेल्या संख्यांना ज्या मोठयात मोठया संख्येने अथवा ज्या विभाजकाने भाग जातो त्या संख्येला अथवा त्या विभाजकला त्यांचा मसावि म्हणतात.

32 चे मूळ अवयव :

$\begin{array}{r|l}2 & 32 \\\cline{1-2} 2 & 16 \\\cline{1-2} 2 & 8 \\ \cline{1-2} 2 & 4 \\\cline{1-2} 2 & 2 \\\cline{1-2} & 1 \end{array}$

24 चे मूळ अवयव :

$\begin{array}{r|l}2 & 24 \\\cline{1-2} 2 & 12 \\\cline{1-2} 2 & 6 \\ \cline{1-2} 3 & 3 \\\cline{1-2} & 1 \end{array}$

48 चे मूळ अवयव :

$\begin{array}{r|l} 2 & 48 \\\cline{1-2} 2 & 24 \\\cline{1-2} 2 & 12 \\ \cline{1-2} 2 & 6 \\\cline{1-2} 3 & 3 \\\cline{1-2} & 1\end{array}$

→ 32 = 2 × 2 × 2 × 2 × 2 × 2

→ 24 = 2 × 2 × 2 × 3

→ 48 = 2 × 2 × 2 × 2 × 3

सामाईक अवयव = 2 × 2 × 2

$\tt{\implies2 \times 2 \times 2}$

$\tt{\implies4 \times 2}$

$\tt{\implies8}$

$\therefore$मसावि = 8

$\textbf{\large{\underline{Question :-}}}$

Find the LCM and HCF of 32, 24, 48

$\textbf{\large{\underline{Answer :-}}}$

LCM = 96

HCF = 8

$\textbf{\large{\underline{Explanation :-}}}$

LCM of 32,24 and 48$\textsf{\underline{}}$

$\begin{array}{r|l}2 & 32,48,24 \\\cline{1-2} 2 & 16,24,12 \\\cline{1-2} 2 & 8,12,6\\ \cline{1-2} 2 & 4,6,3\\\cline{1-2} 2& 2,3,3\\\cline{1-2}3&1,3,3\\\cline{1-2}&1,1,1\end{array}$

LCM = 2 × 2 × 2 × 2 × 2 × 3

$\tt{\implies2 \times 2 \times 2 \times 2 \times 2 \times 3}$

$\tt{\implies4 \times 4 \times 6}$

$\tt{\implies16 \times 4}$

$\tt{\implies96}$

$\therefore$LCM is 96

HCF of 32,24 and 48 $\textsf{\underline{}}$

$\textsf{\underline{32's Prime Factorization :}}$

$\begin{array}{r|l}2 & 32 \\\cline{1-2} 2 & 16 \\\cline{1-2} 2 & 8 \\ \cline{1-2} 2 & 4 \\\cline{1-2} 2 & 2 \\\cline{1-2} & 1 \end{array}$

$\textsf{\underline{24's Prime Factorization :}}$

$\begin{array}{r|l}2 & 24 \\\cline{1-2} 2 & 12 \\\cline{1-2} 2 & 6 \\ \cline{1-2} 3 & 3 \\\cline{1-2} & 1 \end{array}$

$\textsf{\underline{48's Prime Factorization :}}$

$\begin{array}{r|l} 2 & 48 \\\cline{1-2} 2 & 24 \\\cline{1-2} 2 & 12 \\ \cline{1-2} 2 & 6 \\\cline{1-2} 3 & 3 \\\cline{1-2} & 1\end{array}$

→ 32 = 2 × 2 × 2 × 2 × 2 × 2

→ 24 = 2 × 2 × 2 × 3

→ 48 = 2 × 2 × 2 × 2 × 3

Common Factors = 2 × 2 × 2

$\tt{\implies2 \times 2 \times 2}$

$\tt{\implies4 \times 2}$

$\tt{\implies8}$

$\therefore$The HCF is 8

$\textbf{\large{\underline{LCM is 96}}}$

$\textbf{\large{\underline{HCF is 8}}}$

Answer 2

Answer:

16,32,36,48,56 lasavi