Question

find the HCF an0d LCM using the prime factorisation method 18 and 45​

Answer 1

AnswEr:-

• LCM = 90.

• HCF = 9.

ExplanaTion:-

Given Numbers:-

• 18 and 45.

To Find:-

• The LCM and HCF of the numbers by Prime Factorization Method.

So lets Find out:-

1) LCM:-

$\\ \begin{array}{r | l}2 & 18, 45\\ \cline{2-2} 3 & 9, 45 \\ \cline{2-2} 3 & 3, 15 \\ \cline{2-2} 5 & 1, 5\\ \cline{2-2} & 1, 1 \\ \end{array}$

$\\ \bf{ \therefore \: \: LCM =2 \times3 \times 3 \times 5. } \\ \\ \bf{ = 2 \times 3 \times 15 .} \\ \\ \bf{ =2 \times 45. } \\ \\ \boxed{\bf{ = 90.}}$

2. HCF:-

$\\ \begin{array}{r | l}2 & 18\\ \cline{2-2} 3 & 9 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \end{array}\\ \\ \rm and \\ \\ \begin{array}{r | l}3 & 45 \\ \cline{2-2} 3 & 15 \\ \cline{2-2} 5 & 5 \\ \cline{2-2} & 1 \\\end{array}$

$\\ \\ \bf{ \therefore \: \: HCF =3 \times 3. } \\ \\ \boxed{\bf = 9.}$

So LCM and HCF of given numbers are 9 and 90 respectively.