LCM from Prime Decomposition/Examples/111 and 1221

Example of Use of LCM from Prime Decomposition

The lowest common multiple of $111$ and $1221$ is:

$\lcm \set {111, 1221} = 1221$

$\ds 111$

$=$

$\ds 3 \times 37$

$\ds 1221$

$=$

$\ds 3 \times 11 \times 37$

$\ds \leadsto \ \ $

$\ds 111$

$=$

$\ds 3^1 \times 11^0 \times 37^1$

$\ds 1221$

$=$

$\ds 3^1 \times 11^1 \times 37^1$

$\ds \leadsto \ \ $

$\ds \lcm \set {111, 1221}$

$=$

$\ds 3^1 \times 11^1 \times 37^1$

$\ds $

$=$

$\ds 1221$

$\blacksquare$

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