LCM from Prime Decomposition/Examples/111 and 1221

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Example of Use of LCM from Prime Decomposition

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

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


Proof

\(\ds 111\) \(=\) \(\ds 3 \times 37\)
\(\ds 1221\) \(=\) \(\ds 3 \times 11 \times 37\)
\(\ds \leadsto \ \ \) \(\ds 111\) \(=\) \(\ds 3^1 \times 11^0 \times 37^1\)
\(\ds 1221\) \(=\) \(\ds 3^1 \times 11^1 \times 37^1\)
\(\ds \leadsto \ \ \) \(\ds \lcm \set {111, 1221}\) \(=\) \(\ds 3^1 \times 11^1 \times 37^1\)
\(\ds \) \(=\) \(\ds 1221\)

$\blacksquare$


Sources