LCM Sudoku

By |2018-05-06T03:20:33+00:00December 10th, 2008|All Puzzles, Sudoku Puzzles|2 Comments

LCM Sudoku is another Sudoku variant, and this one is based upon the arithmetic and number theory, the least common multiple (LCM).

Rules of LCM Sudoku are like the standard Sudoku, this Sudoku has three basic rules:
1. Each column, each row and each box (3×3 sub grid) must have the numbers 1 through 9.
2. No column, row or box can have two squares with the same number.
3. The puzzle can be solved by finding the values of the 9 given variables in the squares of the 9×9 grid.

At the bottom and right side of the 9×9 grid are numbers, each of which is the Least Common Multiple (LCM) of the given variables in the corresponding column or row of the 9×9 grid.

Altogether 16 Least Common Multiples of 16 groups of variables are given as clues for solving the puzzle. As an example, the LCM of 8, 9, 6, 4, 2, 5 and 7 is 2520. The LCM of the variables v, c, b and n in the seventh column beginning from the left of the 9×9 grid is 252, while the LCM of the variables b, w, m and c in the fourth row beginning from the top of the 9×9 grid is 504.

After finding the values of all the variables, the puzzle is solved by the usual Sudoku technique and strategy.

You can find LCM Sudoku and much more free mathematics enrichment materials, like problems, articles and games at the NRICH Project website, which is part of the University of Cambridge. Happy Puzzling!

Tags: Sudoku

About the Author:

A person with a love and passion for puzzles.


  1. karin December 19, 2008 at 17:11

    i must say your article is really enlightening.I love to play Sudoku, recently i have been playing Gemsweeper, nonogram puzzle from The game is similar to Sudoku but different in a way.Gemsweeper has colourful graphics, is easy to use and 225 ind bending puzzles to solve.This is for all Sudoku loevrs. try it

  2. passionforpuzzles January 3, 2009 at 15:48

    Hi Karen,

    Thanks for the link and I am sure our readers will try out your suggestion.


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