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## 'LCM Sudoku II' printed from http://nrich.maths.org/

#### By Henry Kwok

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### Rules of LCM Sudoku

Like the standard sudoku, this sudoku variant has the basic
rule:

- Every row, every column and every $3\times 3$ box in the grids
contains the digits $1$ through $9$.

The puzzle can be solved by finding the values of the unknown
digits (all indicated by asterisks) in the squares of the $9\times
9$ grid. At the bottom and right side of the $9\times 9$ grid are
numbers, each of which is the Least Common Multiple (LCM) of a
column or row of unknown digits marked by asterisks.

Altogether $18$ Least Common Multiples of $9$ columns and $9$
rows of unknown digits are given as clues for solving the
puzzle.

As an example, the LCM of $3$, $9$, $6$, $4$, $2$ and $1$ is
$36$. In the puzzle, the LCM of the four unknown digits in the
second column beginning from the left of the $9\times 9$ grid is
$36$, while the LCM of the four unknown digits in the seventh row
beginning from the top of the $9\times 9$ grid is $120$.

After finding the values of all the unknown digits, the puzzle
is solved by the usual sudoku technique and strategy.