Lowest Common Multiple of Integers/Examples/-12 and 30

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Example of Lowest Common Multiple of Integers

The lowest common multiple of $-12$ and $30$ is:

$\lcm \set {-12, 30} = 60$


Proof

From Greatest Common Divisor: $-12$ and $30$:

$\gcd \set {-12, 30} = 6$

Then:

\(\ds \lcm \set {-12, 30}\) \(=\) \(\ds \dfrac {12 \times 30} {\gcd \set {-12, 30} }\) Product of GCD and LCM
\(\ds \) \(=\) \(\ds \dfrac {\paren {6 \times 2} \times \paren {6 \times 5} } 6\)
\(\ds \) \(=\) \(\ds 2 \times 5 \times 6\)
\(\ds \) \(=\) \(\ds 60\)

$\blacksquare$


Sources