Question

Answer these two questions pls

Answer 1

${\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}$

$\diamond\:{\boxed{\tt{\purple{{ part \:(i) :}}}}}$

❍ Prime factorisation :-

‣ Prime factors of 12 -

$\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&12 \\\hline 2&6 \\ \hline 3&3\\ \hline &1\end{array}} \end{gathered}\end{gathered}$

‣ Prime factors of 18 -

$\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&18 \\\hline 3&9\\\hline 3&3 \\ \hline &1\end{array}} \end{gathered}\end{gathered}$

Therefore,

$\star \: 12 = {2}^{2} \times {3}^{1}$

$\star \: 18= {2}^{1} \times {3}^{2}$

✧ LCM of 12 and 18 = $\sf {2}^{2} \times {3}^{2}$

$\implies 36$

✧ HCF of 12 and 18 = $\sf {2}^{1} \times {3}^{1}$

$\implies 6$

$\diamond\:{\boxed{\tt{\red{{ part \:(ii) :}}}}}$

❍ Prime factorisation :-

‣ Prime factors of 12 -

$\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&12 \\\hline 2&6 \\ \hline 3&3\\ \hline &1\end{array}} \end{gathered}\end{gathered}$

‣ Prime factors of 15 -

$\begin{gathered}\begin{gathered}{\begin{array}{ c|c}3&15 \\\hline 5&5 \\ \hline &1\end{array}} \end{gathered}\end{gathered}$

‣ Prime factors of 21 -

$\begin{gathered}\begin{gathered}{\begin{array}{ c|c}3&21 \\\hline 7&7 \\ \hline &1\end{array}} \end{gathered}\end{gathered}$

Therefore,

$\star \: 12 = {2}^{2} \times {3}^{1}$

$\star \: 15 = {3}^{1} \times {5}^{1}$

$\star \: 21 = {3}^{1} \times {7}^{1}$

✧ LCM of 12, 15 and 21 = $\sf {2}^{2} \times {3}^{1} \times {5}^{1} \times {7}^{1}$

$\implies 420$

✧ HCF of 12, 15 and 21 = $\sf {3}^{1}$

$\implies 3$

${\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}$

Using,

LCM × HCF = Product of two given numbers

Putting the values,

$\longrightarrow \sf 48 \times 12 = 16 \times y$

$\longrightarrow \sf \dfrac{ \cancel{48} _{3} \times 12}{ \cancel{16}{ _1} } = y$

$\longrightarrow \sf y = 3 \times 12$

$\longrightarrow {\sf{{{\boxed{\green{\bold {\sf y = 36 }}}}}}}$

Therefore,

The value of y = 36

${\large{\textsf{\textbf{\underline{\underline{Important \: points :}}}}}}$

• A natural number "P" > 1 having only two factor one and "P" itself is called prime number.

• A prime number is never negative.

• H.C.F is the product of smallest power of each common prime factor.

• L.C.M is the product of greatest power of each prime factor.

• HCF is always a factor of LCM.

$\underline{\rule{300pts}{3pt}}$