Question

Find the L.C.M of the following by prime factorisation method:
(i) 42, 63, 162
(ii) 42, 78, 104, 112

Answer 1

1)1134

2)4368

Step-by-step explanation:

Plzz mark me as brainliest

Answer 2

Question:-

$\odot$ Find the L.C.M of the following by prime factorisation method:-

• (i) 42, 63, 162
• (ii) 42, 78, 104, 112

Answer:-

(i) 42, 63, 162.

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

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

$\begin {array} {r | l} 2 & 162 \\ 3 & 81 \\ 3 & 27 \\ 3 & 9 \\ 3 & 3 \\ & 1 \end {array}$

$\implies \tt 42 = 2 \times 3 \times 7$

$\implies \tt 63 = 3 \times 3 \times 7$

$\implies \tt 162 = 2 \times 3 \times 3 \times 3 \times 3$

So the LCM is 1134

__________________________________

(ii) 42, 78, 104, 112

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

$\begin {array} {r | l} 2 & 78 \\ 3 & 39 \\ 13 & 13 \\ & 1 \end {array}$

$\begin {array} {r | l} 2 & 104 \\ 2 & 52 \\ 2 & 26 \\ 13 & 13 \\ & 1 \end {array}$

$\begin {array} {r | l} 2 & 112 \\ 2 & 56 \\ 2 & 28 \\ 2 & 14 \\ 7 & 7 \\ & 1 \end {array}$

$\implies \tt 42 = 2 \times 3 \times 7$

$\implies \tt 78 = 2 \times 3 \times 13$

$\implies \tt 104 = 2 \times 2 \times 2 \times 13$

$\implies \tt 112 = 2 \times 2 \times 2 \times 2 \times 7$

So, the LCM is 30,576

Finally we are done with the problem