LCM from Prime Decomposition/Examples/125 and 150

Example of Use of LCM from Prime Decomposition

The lowest common multiple of $125$ and $150$ is:

$\lcm \set {125, 150} = 750$

$\ds 125$

$=$

$\ds 5^3$

$\ds 150$

$=$

$\ds 2 \times 3 \times 5^2$

$\ds \leadsto \ \ $

$\ds 125$

$=$

$\ds 2^0 \times 3^0 \times 5^3$

$\ds 150$

$=$

$\ds 2^1 \times 3^1 \times 5^2$

$\ds \leadsto \ \ $

$\ds \lcm \set {125, 150}$

$=$

$\ds 2^1 \times 3^1 \times 5^3$

$\ds $

$=$

$\ds 750$

$\blacksquare$

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