Lowest Common Multiple of Integers/Examples/7, 9, 12, 14

Example of Lowest Common Multiple of Integers

The lowest common multiple of $7$, $9$, $12$ and $14$ is:

$\lcm \set {7, 9, 12, 14} = 252$

Proof

\(\ds 7\)

\(=\)

\(\ds 7^1\)

\(\ds 9\)

\(=\)

\(\ds 3^2\)

\(\ds 12\)

\(=\)

\(\ds 2^2 \times 3\)

\(\ds 14\)

\(=\)

\(\ds 2 \times 7\)

\(\ds \lcm \set {7, 9, 12, 14}\)

\(=\)

\(\ds 2^2 \times 3^2 \times 7\)

LCM from Prime Decomposition

\(\ds \)

\(=\)

\(\ds 252\)

Hence the result.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): common multiple
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): common multiple