LCM from Prime Decomposition/Examples/253 and 506

Example of Use of LCM from Prime Decomposition

The lowest common multiple of $253$ and $506$ is:

$\lcm \set {253, 506} = 506$

$\ds 253$

$=$

$\ds 11 \times 23$

$\ds 506$

$=$

$\ds 2 \times 11 \times 23$

$\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 $

$=$

$\ds 506$

$\blacksquare$

1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-4}$ The Fundamental Theorem of Arithmetic: Exercise $9 \ \text {(d)}$