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
- 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.3$ The Euclidean Algorithm