Question

Find LCM of the following by Prime-factorisation met
(h) 5, 15, 35
(a) 35, 25
(b) 12, 26
(d) 25, 30, 70
(e) 16, 18, 36

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Answer 1

Correct Question:-

Find LCM of the following by Prime-factorisation method

(a) 5, 15, 35

(b) 35, 25

(c) 12, 26

(d) 25, 30, 70

(e) 16, 18, 36

Solution:-

(a) 5, 15, 35

$\begin{array}{r|l}5 & 5 \\ \cline{2-2} & 1\end{array}$

→ 5 = 5 × 1

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

→ 15 = 3 × 5

$\begin{array}{r|l}5 & 35 \\ \cline{2-2}7 & 7 \\ \cline{2-2} & 1\end{array}$

→ 35 = 5 × 7

•°• LCM of 5, 15, 35 = 3 × 5 × 7

= 105

_________

(b) 35, 25

$\begin{array}{r|l}5 & 35 \\ \cline{2-2}7 & 7 \\ \cline{2-2} & 1\end{array}$

→ 35 = 5 × 7

$\begin{array}{r|l}5 & 25 \\ \cline{2-2}5 & 5 \\ \cline{2-2} & 1\end{array}$

→ 25 = 5 × 5

•°• LCM of 35, 25 = 5 × 5 × 7

= 175

__________

(c) 12, 26

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

→ 12 = 2 × 2 × 3

$\begin{array}{r|l}2 & 26 \\ \cline{2-2}13 & 13 \\ \cline{2-2} & 1\end{array}$

→ 26 = 2 × 13

•°• LCM of 12, 26 = 2 × 2 × 3 × 13

= 156

__________

(d) 25, 30, 70

$\begin{array}{r|l}5 & 25 \\ \cline{2-2}5 & 5 \\ \cline{2-2} & 1\end{array}$

→ 25 = 5 × 5

$\begin{array}{r|l}2 & 30 \\ \cline{2-2}3 & 15 \\ \cline{2-2} 5 & 5 \\ \cline{2-2} & 1\end{array}$

→ 30 = 2 × 3 × 5

$\begin{array}{r|l}2 & 70 \\ \cline{2-2}5 & 35 \\ \cline{2-2} 7 & 7 \\ \cline{2-2} & 1\end{array}$

→ 70 = 2 × 5 × 7

•°• LCM of 25, 30, 70 = 2 × 3 × 5 × 5 × 7

= 1050

__________

(e) 16, 18, 36

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

→ 16 = 2 × 2 × 2 × 2

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

→ 18 = 2 × 3 × 3

$\begin{array}{r|l}2 & 36 \\ \cline{2-2}2 & 18 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \end{array}$

→ 36 = 2 × 2 × 3 × 3

•°• LCM of 16, 18, 36 = 2 × 2 × 2 × 2 × 3 × 3

= 144

Answer 2

$\large\underline\mathfrak{Solution-}$

1). 5, 15, 35

Prime factors :

5 = 5 × 1

15 = 3 × 5 × 1

35 = 5 × 7 × 1

LCM :

3 × 5 × 7

$\implies$ LCM of 5, 15, 35 = 105

___________________

2). 35, 25

Prime factors :

35 = 5 × 7 × 1

25 = 5 × 5 × 1

LCM :

5 × 5 × 7

$\implies$ LCM of 35 and 25 = 175

___________________

3). 12, 26

Prime factors :

12 = 2 × 2 × 3 × 1

26 = 2 × 13 × 1

LCM :

2 × 2 × 3 × 13

$\implies$ LCM of 12 and 26 = 156

___________________

4). 25, 30, 70

Prime factors :

25 = 5 × 5 × 1

30 = 2 × 3 × 5 × 1

70 = 2 × 5 × 7 × 1

LCM :

2 × 3 × 5 × 5 × 7

$\implies$ LCM of 25, 30 and 70 = 1050

___________________

5). 16, 18, 36

Prime factors :

16 = 2 × 2 × 2 × 2 × 1

18 = 2 × 3 × 3

36 = 2 × 2 × 3 × 3

LCM :

2 × 2 × 2 × 2 × 3 × 3

$\implies$ LCM of 16, 18 and 36 = 144