LCM from Prime Decomposition/Examples/253 and 506
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Example of Use of LCM from Prime Decomposition
The lowest common multiple of $253$ and $506$ is:
- $\lcm \set {253, 506} = 506$
Proof
| \(\ds 253\) | \(=\) | \(\ds 11 \times 23\) | ||||||||||||
| \(\ds 506\) | \(=\) | \(\ds 2 \times 11 \times 23\) | ||||||||||||
| \(\ds \leadsto \ \ \) | \(\ds 253\) | \(=\) | \(\ds 2^0 \times 11^1 \times 23^1\) | |||||||||||
| \(\ds 506\) | \(=\) | \(\ds 2^1 \times 11^1 \times 23^1\) | ||||||||||||
| \(\ds \leadsto \ \ \) | \(\ds \lcm \set {253, 506}\) | \(=\) | \(\ds 2^1 \times 11^1 \times 23^1\) | |||||||||||
| \(\ds \) | \(=\) | \(\ds 506\) |
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-4}$ The Fundamental Theorem of Arithmetic: Exercise $9 \ \text {(d)}$