Question

L. C. M


of 112, 168, 266

Answer 1

6384

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Answer 2

Given numbers,

112, 168 and 266.

To find,

LCM(112, 168, 266) = ?

Prime factorisation of 112 is,

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

112 = $2 \times 2 \times 2 \times 2 \times 7$ -----(i)

112 = $2^4 \times 7$

Prime factorisation of 168 is,

$\begin{array}{r | l} 2 & 168 \\ \cline{1-2} 2 & 84 \\ \cline{1-2} 2 & 42 \\ \cline{1-2} 3 & 21 \\ \cline{1-2} 7 & 7 \\ \cline{1-2} & 1 \end{array}$

168 = $2 \times 2 \times 2 \times 3 \times 7$ -----(ii)

168 = $2^3 \times 3 \times 7$

Prime factorisation of 266 is,

$\begin{array}{r | l} 2 & 266 \\ \cline{1-2} 7 & 133 \\ \cline{1-2} 19 & 19 \\ \cline{1-2} & 1 \end{array}$

266 = $2 \times 7 \times 19$ ------(iii)

From equation (i), (ii) and (iii),

112 = $2 \times 2 \times 2 \times 2 \times 7$

168 = $2 \times 2 \times 2 \times 3 \times 7$

266 = $2 \times 7 \times 19$

LCM(112, 168, 266) = $2 \times 2 \times 2 \times 3 \times 7 \times 19$

$\boxed{\bold{LCM(112, 168, 266) = 6,384}}$