LCM from Prime Decomposition/Examples/132 and 154

Example of Use of LCM from Prime Decomposition

The lowest common multiple of $132$ and $154$ is:

$\lcm \set {132, 154} = 924$

$\ds 132$

$=$

$\ds 2^2 \times 3 \times 11$

$\ds 154$

$=$

$\ds 2 \times 7 \times 11$

$\ds \leadsto \ \ $

$\ds 132$

$=$

$\ds 2^2 \times 3^1 \times 7^0 \times 11^1$

$\ds 154$

$=$

$\ds 2^1 \times 3^0 \times 7^1 \times 11^1$

$\ds \leadsto \ \ $

$\ds \lcm \set {132, 154}$

$=$

$\ds 2^2 \times 3^1 \times 7^1 \times 11^1$

$\ds $

$=$

$\ds 924$

$\blacksquare$

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