Question

find the l.c.m and h. c. f of 12,18 and 36 by using prime factorisation​

Answer 1

Step-by-step explanation:

$\begin{array}{c|c}12&2\\6&2\\3&3\\1\end{array}\qquad\begin{array}{c|c}18&2\\9&3\\3&3\\1\end{array}\qquad\begin{array}{c|c}36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\12=\boxed{2}\cdot2\cdot\boxed{3}\\\\18=\boxed{2}\cdot\boxed{3}\cdot3\\\\36=\boxed{2}\cdot2\cdot\boxed{3}\cdot3\\\\LCM(12,\ 18,\ 36)=\boxed{2}\cdot\boxed{3}\cdot2\cdot3=36\\\\HCF(12,\ 18,\ 36)=\boxed{2}\cdot\boxed{3}=6$

Answer 2

Answer:

L.C.M (12,18,36)= 36,

H.C.F (12, 18, 36)= 6

Explanation:

L.C.M of 12, 18, 36 by prime factorisation:

2 | 12, 18, 36

2 | 6, 9, 18

3 | 3, 9, 9

3 | 1, 3, 3

   | 1, 1, 1

= 2× 2 × 3 × 3

= 2² × 3²

= 4 × 9

= 36

Prime factorisation of 12:

2 | 12

2 | 6

3 | 3

1  | 1

= 2 × 2 × 3

=2² × 3

Prime Factorisation of 18:

2 | 18

3 | 9

3 | 3

1  | 1

= 2 × 3 × 3

= 2 × 3²

Prime Factorisation of 36:

2 | 36

2 | 18

3 | 9

3 | 3

1  | 1

= 2 × 2 × 3 × 3

= 2² × 3²

H.C.F (12, 18, 36 )= 2 × 3 = 6                 [ Least power of the factors ]

Hence, proved.

Hope you got that.

Thank You.