# Common Multiples

Student View (Opens in new window) # Lesson Overview

Students use a geometric model to investigate common multiples and the least common multiple of two numbers.

# Key Concepts

A geometric model can be used to investigate common multiples. When congruent rectangular cards with whole-number lengths are arranged to form a square, the length of the square is a common multiple of the side lengths of the cards. The least common multiple is the smallest square that can be formed with those cards.

For example, using six 4 × 6 rectangles, a 12 × 12 square can be formed. So, 12 is a common multiple of both 4 and 6. Since the 12 × 12 square is the smallest square that can be formed, 12 is the least common multiple of 4 and 6.

Common multiples are multiples that are shared by two or more numbers. The least common multiple (LCM) is the smallest multiple shared by two or more numbers.

# Goals and Learning Objectives

• Use a geometric model to understand least common multiples.
• Find the least common multiple of two whole numbers equal to or less than 12.