LCM Sudoku II

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

Age
11 to 18
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



 

By Henry Kwok

 

 

LCM Sudoku II

 

 

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.