Plastic construction bricks of different dimensions can represent factorized numbers. A 2-by-3 brick, for example, represents the number six divided into its factors, represented by the length and width. Provide students with a large number of bricks in two sizes, such as 2-by-4 and 1-by-3. Tell them to experiment until they manage to build two matching rectangles, one out of each size of brick. The size of the resulting rectangles will show a common denominator. In this case a 3-by-8 rectangle, representing 24, is the smallest rectangle that can be made from either 2-by-4 or 1-by-3 bricks.
Repeating mechanical steps will lead some students to understanding. Divide each number into two factors, writing them at the end of an upside-down V. Repeat until you find all the prime factors. For each tree, write each prime number that appears in the tree, then write a small number (exponent) to indicate how many times each prime number appears in the tree. To find the LCD of all the trees, write a list containing each prime number that appears anywhere on the page, then add the biggest exponent each prime has anywhere on the page and multiply the results out.
Chopped fruit can illustrate LCDs in a vivid and relevant manner that will help some students see the application of the abstract mathematical concepts. To efficiently divide apples equally between students, you need to cut the apples into a number of pieces that equals the LCD of the number of students and the number of apples. To divide six apples evenly between 15 students, calculate that the LCD is 30, then cut each apple into five pieces (30 pieces total) and give each student two. Show that this is more efficient than cutting each apple into 15 pieces.
Number lines offer another way to visualize LCDs. Draw two number lines, aligned one over the other, whose ranges stretch from zero to beyond the LCD of two numbers. Mark intervals of the first number on one number line and intervals of the second number on the other number line. The marks will first line up with each other at the LCD. For example, if you make a mark every 6 units on one number line and every 9 units on another, the marks will first line up at 18, the LCD of 6 and 9.