Common Multiples

The Smallest Square

Work Time

The Smallest Square

Think about the smallest square you made using the 4 x 6 rectangles.

  • How many rectangles high is the square?
  • How many rectangles wide is the square?
  • Why did you use more rectangles in one direction than in the other direction?
  • How long is one side of the square?
  • How do you know that the square is the smallest square you can make?
  • The side lengths of all of the squares are the common multiples of 4 and 6. The side length of the smallest square is the least common multiple (LCM) of 4 and 6. Why would you build squares rather than rectangles to find the least common multiple?

INTERACTIVE: Build Squares with Rectangles