Question

6 8 12
$lcm$
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Answer 1

Question:

Find the LCM of 6, 8 and 12.

Answer:

$\fbox{\bold{LCM(6,8,12) = 24}}$

Step-by-step explanation:

The prime factorisation of 6 is,

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

The prime factorisation of 6 = $2 \times 3$

The prime factorisation of 8,

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

The prime factorisation of 8 = $2 \times 2 \times 2$

The prime factorisation of 12 is,

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

The prime factorisation of 12 = $2 \times 2 \times 3$

Factors(6) = $2 \times 3$

Factors(8) = $2 \times 2 \times 2$

Factors(12) = $2 \times 2 \times 3$

Now LCM of 6, 8 and 12,

LCM(6,8,12) = $2 \times 2 \times 2 \times 3$

$\fbox{\bold{LCM(6,8,12) = 24}}$